# Khan/khan-exercises

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 34ddff1 New exercise: systems of equations word problems elizabethslavitt authored Dec 12, 2011 1 cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 2 3 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 4 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 5 Systems of equations word problems ac1415e Use requirejs for module loading spicyj authored Mar 5, 2014 6 34ddff1 New exercise: systems of equations word problems elizabethslavitt authored Dec 12, 2011 7 8 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 9
875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 10
4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 11
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13 randRange( 0, 2 ) 14 [randRange( 2, 4 ), randRange( 2, 4 ), randRange( 40, 50 )][INDEX] 15 [randRange( X + 2, 10 ), randRange( X + 2, 10 ), randRange( 30, 50 )][INDEX] 16 randRange( 0, 1 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 17 randRange( 0, 1 ) 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 18 [roundTo( 8, randRange( 5, 8 ) + CENT_1 * 0.5 ), roundTo( 8, randRange( 5, 8 ) + CENT_1 * 0.5 ), 1][INDEX] 19 [roundTo( 8, randRange( 2, 4 ) + CENT_2 * 0.5 ), roundTo( 8, randRange( 2, 4 ) + CENT_2 * 0.5 ), 1][INDEX] 20 roundTo( 8, A1 * X + B1 * Y ) 21 1 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 22 [-1, -1, randRange( -4, -2 )][INDEX] 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 23 roundTo( 8, A2 * X + B2 * Y ) 24 A1 * C2 > 0 ? "-" : "+" 25 B1 * Y > 0 ? "-" : "+" de19411 Manually i18nize all of the minor exercises xymostech authored Jun 3, 2013 26 [ 27 \$._("A group of adults and kids went to see a movie"), 28 \$._("A few families took a trip to an amusement park together"), 29 "" 30 ][INDEX] 31 [ 32 \$._("Find the number of adults and kids in the group"), 33 \$._("Find the number of adults and kids on the trip"), 34 "" 35 ][INDEX] 36 [ 37 \$._("adults"), 38 \$._("adults"), 39 \$._("home team fans") 40 ][INDEX] 41 [ 42 \$._("kids"), 43 \$._("kids"), 44 \$._("away team fans") 45 ][INDEX] 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 46
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 48
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PROBLEM_1. Tickets cost \$localeToFixed(A1, 2) each for adults and \$localeToFixed(B1, 2) each for kids, and the group paid \$localeToFixed(C1, 2) in total. There were abs(C2) fewer adults than kids in the group.

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PROBLEM_2.

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C1 people attended a baseball game. Everyone there was a fan of either the home team or the away team. 54 The number of home team fans was abs(C2) less than abs(B2) times the number of away team fans.

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How many home team and away team fans attended the game?

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4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 57
0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 58
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# of UNIT_1 = X

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# of UNIT_2 = Y

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 61
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Let x equal the number of UNIT_1 and y equal the number of UNIT_2.

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The system of equations is then:

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 66

\blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}
67 \green{x = expr(["+", ["*", -B2, "y"], C2])}

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Solve for x and y using substitution.

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4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 70
875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 71

Since x has already been solved for, substitute \green{expr(["+", ["*", -B2, "y"], C2])} for x in the first equation.

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\blue{A1-}\green{(expr(["+", ["*", -B2, "y"], C2]))}\blue{+ expr(["*", B1, "y"]) = C1}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 73
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Simplify and solve for y.

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 76

77 expr(["+", ["*", roundTo(8, A1 * -B2), "y"], roundTo(8, A1 * C2)]) + expr(["*", B1, "y"]) = C1 78

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80 expr(["+", ["*", roundTo(8, A1 * -B2 + B1), "y"], roundTo(8, A1 * C2)]) = C1 81

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83 expr(["*", roundTo(8, A1 * -B2 + B1), "y"]) = roundTo(8, C1 - A1 * C2) 84

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86 y = \dfrac{roundTo(8, C1 - A1 * C2)}{roundTo( 8, A1 * -B2 + B1 )} 87

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\orange{y = Y}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 89
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 91

Now that you know \orange{y = Y}, plug it back into \green{x = expr(["+", ["*", -B2, "y"], C2])} to find x.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 92
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 94

\green{x = -B2-}\orange{(Y)}\green{ + C2}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 95

x = -B2 * Y + C2

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 96

\red{x = X}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 97
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 99

You can also plug \orange{y = Y} into \blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1} and get the same answer for x:

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\blue{expr(["*", A1, "x"]) + B1-}\orange{(Y)}\blue{= C1}

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\red{x = X}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 102
875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 103

There were X UNIT_1 and Y UNIT_2.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 104
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108 randRange( 0, 2 ) 109 [randRange( 2, 4 ), randRange( 2, 4 ), randRange( 40, 50 )][INDEX] 110 [randRange( X + 2, 10 ), randRange( X + 2, 10 ), randRange( 30, 50 )][INDEX] 111 randRange( 0, 1 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 112 randRange( 0, 1 ) 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 113 [roundTo( 8, randRange( 5, 8 ) + CENT_1 * 0.5 ), roundTo( 8, randRange( 5, 8 ) + CENT_1 * 0.5 ), 1][INDEX] 114 [roundTo( 8, randRange( 2, 4 ) + CENT_2 * 0.5 ), roundTo( 8, randRange( 2, 4 ) + CENT_2 * 0.5 ), 1][INDEX] 115 roundTo( 8, A1 * X + B1 * Y ) 116 1 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 117 [-1, -1, randRange( -4, -2 )][INDEX] 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 118 roundTo( 8, A2 * X + B2 * Y ) 119 B1 * C2 > 0 ? "-" : "+" 120 A1 * X > 0 ? "-" : "+" de19411 Manually i18nize all of the minor exercises xymostech authored Jun 4, 2013 121 [ 122 \$._("The drama club sold bags of candy and cookies to raise money for the spring show"), 123 \$._("A local gift shop sold bags of candy and cookies for Halloween"), 124 "" 125 ][INDEX] 126 [ 127 \$._("Find the number of bags of candy and cookies sold by the drama club"), 128 \$._("Find the number of bags of candy and cookies sold by the gift shop"), 129 "" 130 ][INDEX] 131 [ 132 \$._("bags of candy"), 133 \$._("bags of candy"), 134 \$._("angle 1") 135 ][INDEX] 136 [ 137 \$._("bags of cookies"), 138 \$._("bags of cookies"), 139 \$._("angle 2") 140 ][INDEX] 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 141
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 143
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PROBLEM_1. Bags of candy cost \$localeToFixed(A1, 2), and bags of cookies cost \$localeToFixed(B1, 2), and sales equaled \$localeToFixed(C1, 2) in total. There were C2 more bags of cookies than candy sold.

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PROBLEM_2.

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The sum of two angles is C1^\circ. Angle 2 is abs(C2)^\circ smaller than abs(A2) times angle 1.

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What are the measures of the two angles in degrees?

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4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 151
0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 152
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# of UNIT_1 = X

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# of UNIT_2 = Y

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 155
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de19411 Manually i18nize all of the minor exercises xymostech authored Jun 4, 2013 157

158 Let x equal the number of UNIT_1 and y equal the number of UNIT_2. 159

3650bc2 Fix this text right: it was supposed to go in the data-else. csilvers authored Jun 4, 2013 160 Let x equal the measure of UNIT_1 and y equal the measure of UNIT_2.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 161
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The system of equations is then:

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 163

\blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}
164 \green{y = expr(["+", ["*", -A2, "x"], C2])}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 165
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 167

Since we already have solved for y in terms of x, we can use substitution to solve for x and y.

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4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 169
875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 170

Substitute \green{expr(["+", ["*", -A2, "x"], C2])} for y in the first equation.

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\blue{expr(["*", A1, "x"]) + B1-}\green{(expr(["+", ["*", -A2, "x"], C2]))}\blue{= C1}

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Simplify and solve for x.

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 175

176 expr(["+", ["*", A1, "x"], ["*", roundTo(8, B1 * -A2), "x"]]) + roundTo(8, B1 * C2) = C1 177

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179 expr(["+", ["*", roundTo(8, A1 + B1 * -A2), "x"], roundTo(8, B1 * C2)]) = C1 180

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182 expr(["*", roundTo(8, A1 + B1 * -A2), "x"]) = roundTo(8, C1 - B1 * C2) 183

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185 x = \dfrac{roundTo( 8, C1 - B1 * C2 )}{roundTo(8, A1 + B1 * -A2)} 186

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\red{x = X}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 188
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 190

Now that you know \red{x = X}, plug it back into \green{y = expr(["+", ["*", -A2, "x"], C2])} to find y.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 191
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 193

\green{y = -A2-}\red{(X)}\green{ + C2}

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y = roundTo(8, -A2 * X) + C2

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\orange{y = Y}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 196
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 198

You can also plug \red{x = X} into \blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1} and get the same answer for y:

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\blue{A1-}\red{(X)}\blue{ + expr(["*", B1, "y"]) = C1}

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\orange{y = Y}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 201
de19411 Manually i18nize all of the minor exercises xymostech authored Jun 4, 2013 202

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 203 X bags of candy and Y bags of cookies were sold. de19411 Manually i18nize all of the minor exercises xymostech authored Jun 4, 2013 204

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 205 The measure of angle 1 is X^\circ and the measure of angle 2 is Y^\circ. de19411 Manually i18nize all of the minor exercises xymostech authored Jun 4, 2013 206

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 207
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0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 210
4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 211 randRange( 2, 4 ) 212 randRange( X + 2, 10 ) 213 1 214 randRange( 0, 1 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 215 randRange( 0, 1 ) 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 216 roundTo( 8, randRange( 100, 300 ) / 100 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 217 INDEX === 0 ? -1 * Z1 : randRangeWeighted( -4, 4, -1, 0 ) * Z1 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 218 roundTo( 8, randRange( 200, 600 ) / 100 ) 219 roundTo( 8, randRange( 200, 600 ) / 100 ) 220 roundTo( 8, randRange( 200, 600 ) / 100 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 221 roundTo( 8, randRange( 200, 600 ) / 100 ) 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 222 roundTo( 8, randRange( 5, 8 ) + CENT_1 * 0.5 ) 223 roundTo( 8, randRange( 2, 4 ) + CENT_2 * 0.5 ) 224 roundTo( 8, A1 * X + B1 * Y ) 225 A1 * randRange( 2, 4 ) 226 roundTo( 8, randRange( 7, 12 ) + ( CENT_1 + CENT_2 ) * 0.5 ) 227 roundTo( 8, A2 * X + B2 * Y ) 228 [ 1, roundTo( 8, -A2 / A1 ), 1, A2 > 0 && A1 < 0 ? A2 : -A2 ][ INDEX ] 229 [ 1, 1, roundTo( 8, -A1 / A2 ), A2 > 0 && A1 < 0 ? -A1 : A1 ][ INDEX ] 230 B1 * Y > 0 ? "-" : "+" 231 B2 * Y > 0 ? "-" : "+" 232
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 234

All of the {3rd|4th|5th} grade teachers and students from school(1) went on a field trip to an {art|archaeology} museum. Tickets were \$localeToFixed(A1, 2) each for teachers and \$localeToFixed(B1, 2) each for students, and the group paid \$localeToFixed(C1, 2) in total.

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{A few weeks later|The next month}, the same group visited a {science|natural history} museum where the tickets cost \$localeToFixed(A2, 2) each for teachers and \$localeToFixed(B2, 2) each for students, and the group paid \$localeToFixed(C2, 2) in total.

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Find the number of teachers and students on the field trips.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 237
0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 238
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# of teachers = X

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# of students = Y

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 241
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Let x equal the number of teachers and y equal the number of students.

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The system of equations is:

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 246

\blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}
247 \green{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 248

Solve for x and y using elimination.

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de19411 Manually i18nize all of the minor exercises xymostech authored Jun 4, 2013 251

252 Multiply the bottom equation by MULT2. 253

254 Multiply the top equation by MULT1 and the bottom equation by MULT2. 255

256 Multiply the top equation by MULT1. 257

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 258

\blue{expr(["+", ["*", A1 * MULT1, "x"], ["*", B1 * MULT1, "y"]]) = C1 * MULT1}
259 \green{expr(["+", ["*", A2 * MULT2, "x"], ["*", B2 * MULT2, "y"]]) = C2 * MULT2}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 260
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 262

Add the top and bottom equations together.

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264 expr(["*", roundTo(8, B1 * MULT1 + B2 * MULT2), "y"]) = roundTo(8, C1 * MULT1 + C2 * MULT2) 265

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267 y = \dfrac{roundTo(8, C1 * MULT1 + C2 * MULT2)}{roundTo(8, B1 * MULT1 + B2 * MULT2)}

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\orange{y = Y}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 269
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 271

Now that you know \orange{y = Y}, plug it back into \blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1} to find x.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 272
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 274

\blue{expr(["*", A1, "x"]) + B1-}\orange{(Y)}\blue{= C1}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 275

expr(["+", ["*", A1, "x"], B1 * Y]) = C1

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 276

expr(["*", A1, "x"]) = roundTo(8, C1 - B1 * Y)

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x = \dfrac{roundTo( 8, C1 - B1 * Y )}{A1}

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\red{x = X}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 279
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 281

You can also plug \orange{y = Y} into \green{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2} and get the same answer for x:

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\green{expr(["*", A2, "x"]) + B2-}\orange{(Y)}\green{= C2}

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\red{x = X}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 284
875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 285

There were X teachers and Y students on the field trips.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 286
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290 randRange( 11, 99 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 291 randRange( 10, X - 1 ) 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 292 0 293 roundTo( 8, randRange( 100, 300 ) / 100 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 294 INDEX === 0 ? -1 * Z1 : randRangeWeighted( -4, 4, -1, 0 ) * Z1 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 295 roundTo( 8, randRange( 200, 600 ) / 100 ) 296 roundTo( 8, randRange( 200, 600 ) / 100 ) 297 roundTo( 8, randRange( 200, 600 ) / 100 ) 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 298 roundTo( 8, randRange( 200, 600 ) / 100 ) 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 299 1 300 [ 1, Z1, Z2, Z5 ][ INDEX ] 301 roundTo( 8, A1 * X + B1 * Y ) 302 1 303 [ -1, Z2, Z1, Z6 ][ INDEX ] 304 roundTo( 8, A2 * X + B2 * Y ) 305 [ 1, roundTo( 8, -B2 / B1 ), 1, B2 > 0 && B1 < 0 ? B2 : -B2 ][ INDEX ] 306 [ 1, 1, roundTo( 8, -B1 / B2 ), B2 > 0 && B1 < 0 ? -B1 : B1 ][ INDEX ] 307 A1 * X > 0 ? "-" : "+" 308 A2 * X > 0 ? "-" : "+" 875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 309 max(X, Y) 310 min(X, Y) 4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 311
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 313

The sum of two numbers is C1, and their difference is C2. What are the two numbers?

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 314
7fab1d8 Whitespace spicyj authored Dec 31, 2011 315 875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 316
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larger number = LARGER

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smaller number = SMALLER

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 319
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Let x be the first number, and let y be the second number.

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The system of equations is:

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 326

\blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1}
327 \green{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 328

Solve for x and y using elimination. e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 329

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 330
de19411 Manually i18nize all of the minor exercises xymostech authored Jun 4, 2013 331

332 Multiply the bottom equation by MULT2. 333

334 Multiply the top equation by MULT1 and the bottom equation by MULT2. 335

336 Multiply the top equation by MULT1. 337

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 338

\blue{expr(["+", ["*", A1 * MULT1, "x"], ["*", B1 * MULT1, "y"]]) = C1 * MULT1}
339 \green{expr(["+", ["*", A2 * MULT2, "x"], ["*", B2 * MULT2, "y"]]) = C2 * MULT2}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 340
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 342

Add the top and bottom equations together.

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344 expr(["*", roundTo(8, A1 * MULT1 + A2 * MULT2), "x"]) = roundTo(8, C1 * MULT1 + C2 * MULT2) 345

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347 x = \dfrac{roundTo(8, C1 * MULT1 + C2 * MULT2)}{roundTo( 8, A1 * MULT1 + A2 * MULT2 )} 348

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\red{x = X}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 350
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 352

Now that you know \red{x = X}, plug it back into \blue{expr(["+", ["*", A1, "x"], ["*", B1, "y"]]) = C1} to find y.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 353
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 355

\blue{A1-}\red{(X)}\blue{ + expr(["*", B1, "y"]) = C1}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 356

expr(["+", A1 * X, ["*", B1, "y"]]) = C1

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expr(["*", B1, "y"]) = roundTo( 8, C1 - A1 * X )

875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 358

\dfrac{expr(["*", B1, "y"])}{\blue{B1}} = \dfrac{roundTo( 8, C1 - A1 * X )}{\blue{B1}}

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\orange{y = Y}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 360
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875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 362

You can also plug \red{x = X} into \green{expr(["+", ["*", A2, "x"], ["*", B2, "y"]]) = C2} and get the same answer for y:

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\green{A2-}\red{(X)}\green{ + expr(["*", B2, "y"]) = C2}

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\orange{y = Y}

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 365
875bee6 Merge pull request #114494 from petercollingridge/system_eq petercollingridge authored Nov 13, 2013 366

Therefore, the larger number is LARGER, and the smaller number is SMALLER.

4e4cb9b lint: tabs->spaces and jQuery->\$ for exercises beneater authored Apr 10, 2012 367
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cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 371 372
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