# Khan/khan-exercises

Hints cleanup

1 parent 319325c commit 12c14db52f66f420bd0177fd1a73e18bb613a2d1 spicyj committed May 31, 2011
135 exercises/age_word_problems.html
 @@ -27,17 +27,12 @@
(C * (B + A) - B) / (C - 1)
-

Let person(1)'s current age be personVar(1).

- -

That means that B years ago, person(1) was personVar(1) - B years old.

- -

person(2) is personVar(1) - A years old right now, so B years ago, he(2) was (personVar(1) - A) - B = personVar(1) - A + B years old.

- -

person(1) was C times as old as person(2), so that means personVar(1) - B = C (personVar(1) - A + B).

- -

Expand: personVar(1) - B = C personVar(1) - C * (A + B).

- -

Solve for personVar(1) to get C - 1 personVar(1) = C * (A + B) - B; personVar(1) = (C * (B + A) - B) / (C - 1).

+

Let person(1)'s current age be personVar(1).

+

That means that B years ago, person(1) was personVar(1) - B years old.

+

person(2) is personVar(1) - A years old right now, so B years ago, he(2) was (personVar(1) - A) - B = personVar(1) - A + B years old.

+

person(1) was C times as old as person(2), so that means personVar(1) - B = C (personVar(1) - A + B).

+

Expand: personVar(1) - B = C personVar(1) - C * (A + B).

+

Solve for personVar(1) to get C - 1 personVar(1) = C * (A + B) - B; personVar(1) = (C * (B + A) - B) / (C - 1).

@@ -52,17 +47,12 @@
(A - B + C * B) / (C - 1)
-

Let person(2)'s current age be personVar(2).

- -

That means that person(1) is currently personVar(2) + A years old and B years ago, person(1) was (personVar(2) + A) - B = personVar(2) + A - B years old.

- -

B years ago, person(2) was personVar(2) - B years old.

- -

person(1) was C times as old as person(2), so that means personVar(2) + A - B = C (personVar(2) - B).

- -

Expand: personVar(2) + A - B = C personVar(2) - C * B.

- -

Solve for personVar(2) to get C - 1 personVar(2) = A - B + C * B; personVar(2) = (A - B + C * B) / (C - 1).

+

Let person(2)'s current age be personVar(2).

+

That means that person(1) is currently personVar(2) + A years old and B years ago, person(1) was (personVar(2) + A) - B = personVar(2) + A - B years old.

+

B years ago, person(2) was personVar(2) - B years old.

+

person(1) was C times as old as person(2), so that means personVar(2) + A - B = C (personVar(2) - B).

+

Expand: personVar(2) + A - B = C personVar(2) - C * B.

+

Solve for personVar(2) to get C - 1 personVar(2) = A - B + C * B; personVar(2) = (A - B + C * B) / (C - 1).

@@ -82,17 +72,12 @@
A * C / (C - 1)
-

Let person(1)'s age be personVar(1).

- -

We know person(2) is 1/C as old as person(1), so person(2)'s age can be written as personVar(1) / C.

- -

His(2) age can also be written as personVar(1) - A.

- -

Set the two expressions for person(2)'s age equal to each other: personVar(1) / C = personVar(1) - A.

- -

Multiply both sides by C to get personVar(1) = C personVar(1) - A * C.

- -

Solve for personVar(1) to get C - 1 personVar(1) = A * C; personVar(1) = A * C / (C - 1).

+

Let person(1)'s age be personVar(1).

+

We know person(2) is 1/C as old as person(1), so person(2)'s age can be written as personVar(1) / C.

+

His(2) age can also be written as personVar(1) - A.

+

Set the two expressions for person(2)'s age equal to each other: personVar(1) / C = personVar(1) - A.

+

Multiply both sides by C to get personVar(1) = C personVar(1) - A * C.

+

Solve for personVar(1) to get C - 1 personVar(1) = A * C; personVar(1) = A * C / (C - 1).

@@ -107,15 +92,11 @@
A / (C - 1)
-

Let person(2)'s age be personVar(2).

- -

We know person(1) is C times as old as person(2), so person(1)'s age can be written as C personVar(2).

- -

His(1) age can also be written as personVar(2) + A.

- -

Set the two expressions for person(1)'s age equal to each other: C personVar(2) = personVar(2) + A.

- -

Solve for personVar(2) to get C - 1 personVar(2) = A; personVar(2) = A / (C - 1).

+

Let person(2)'s age be personVar(2).

+

We know person(1) is C times as old as person(2), so person(1)'s age can be written as C personVar(2).

+

His(1) age can also be written as personVar(2) + A.

+

Set the two expressions for person(1)'s age equal to each other: C personVar(2) = personVar(2) + A.

+

Solve for personVar(2) to get C - 1 personVar(2) = A; personVar(2) = A / (C - 1).

@@ -134,17 +115,7 @@
A * B * (C - 1) / (C - A)
-

Let person(1)'s age be personVar(1).

- -

We know person(2) is 1/A as old as person(1), so person(2)'s age can be written as personVar(1) / A.

- -

B years ago, person(1) was personVar(1) - B years old and person(2) was personVar(1) / A - B years old.

- -

At that time, person(1) was C times as old as person(2), so we can write personVar(1) - B = C (personVar(1) / A - B).

- -

Expand: personVar(1) - B = fraction(C, A) personVar(1) - C * B.

- -

Solve for personVar(1) to get fraction(C - A, A) personVar(1) = B * (C - 1); personVar(1) = fraction(A, C - A) \cdot B * (C - 1) = A * B * (C - 1) / (C - A).

+

Solve for personVar(1) to get fraction(C - A, A) personVar(1) = B * (C - 1); personVar(1) = fraction(A, C - A) \cdot B * (C - 1) = A * B * (C - 1) / (C - A).

@@ -157,17 +128,12 @@
B * (C - 1) / (C - A)
-

Let person(2)'s age be personVar(2).

- -

We know person(1) is A times as old as person(2), so person(1)'s age can be written as A personVar(2).

- -

B years ago, person(1) was A personVar(2) - B years old and person(2) was personVar(2) - B years old.

- -

At that time, person(1) was C times as old as person(2), so we can write A personVar(2) - B = C (personVar(2) - B).

- -

Expand: A personVar(2) - B = C personVar(2) - B * C.

- -

Solve for personVar(1) to get C - A personVar(1) = B * (C - 1); personVar(1) = B * (C - 1) / (C - A).

+

Let person(2)'s age be personVar(2).

+

We know person(1) is A times as old as person(2), so person(1)'s age can be written as A personVar(2).

+

B years ago, person(1) was A personVar(2) - B years old and person(2) was personVar(2) - B years old.

+

At that time, person(1) was C times as old as person(2), so we can write A personVar(2) - B = C (personVar(2) - B).

+

Expand: A personVar(2) - B = C personVar(2) - B * C.

+

Solve for personVar(1) to get C - A personVar(1) = B * (C - 1); personVar(1) = B * (C - 1) / (C - A).

@@ -185,17 +151,11 @@
B / (A - 1)
-

Let person(1)'s age be personVar(1).

- -

In B years, he(1) will be personVar(1) + B years old.

- -

At that time, he(1) will also be A personVar(1) years old.

- -

We write personVar(1) + B = A personVar(1).

- -

Solve for personVar(1) to get A - 1 personVar(1) = B; personVar(1) = B / (A - 1).

- -

+

Let person(1)'s age be personVar(1).

+

In B years, he(1) will be personVar(1) + B years old.

+

At that time, he(1) will also be A personVar(1) years old.

+

We write personVar(1) + B = A personVar(1).

+

Solve for personVar(1) to get A - 1 personVar(1) = B; personVar(1) = B / (A - 1).

@@ -214,28 +174,15 @@
(A - B * C) / (C - 1)
-

Let y be the number of years that it will take.

- -

In y years, person(1) will be A + y years old and person(2) will be B + y years old.

- -

At that time, person(1) will be C times as old as person(2).

- -

We write A + y = C (B + y).

- -

Expand to get A + y = C * B + C y.

- -

Solve for y to get C - 1 y = A - C * B; y = (A - C * B) / (C - 1).

+

Let y be the number of years that it will take.

+

In y years, person(1) will be A + y years old and person(2) will be B + y years old.

+

At that time, person(1) will be C times as old as person(2).

+

We write A + y = C (B + y).

+

Expand to get A + y = C * B + C y.

+

Solve for y to get C - 1 y = A - C * B; y = (A - C * B) / (C - 1).

-
-

-

-

-

-

-

-
25 exercises/average_word_problems.html
 @@ -33,9 +33,9 @@
SUM / LENGTH
-

The average is the sum of his(1) scores divided by the number of scores.

-

There are LENGTH scores and their sum is SCORES.join(" + ") = SUM.

-

His(1) average score is SUM \div LENGTH = SUM / LENGTH.

+

The average is the sum of his(1) scores divided by the number of scores.

+

There are LENGTH scores and their sum is SCORES.join(" + ") = SUM.

+

His(1) average score is SUM \div LENGTH = SUM / LENGTH.

@@ -54,10 +54,10 @@
NEW_AVG + COUNT * (NEW_AVG - OLD_AVG)
-

Let his(1) score on the next exam(1) be x.

-

The sum of all of his(1) scores is then COUNT \cdot OLD_AVG + x.

-

The same sum must also be equal to COUNT + 1 \cdot NEW_AVG.

-

Solve: x = COUNT + 1 \cdot NEW_AVG - COUNT \cdot OLD_AVG = (COUNT + 1) * NEW_AVG - COUNT * OLD_AVG.

+

Let his(1) score on the next exam(1) be x.

+

The sum of all of his(1) scores is then COUNT \cdot OLD_AVG + x.

+

The same sum must also be equal to COUNT + 1 \cdot NEW_AVG.

+

Solve: x = COUNT + 1 \cdot NEW_AVG - COUNT \cdot OLD_AVG = (COUNT + 1) * NEW_AVG - COUNT * OLD_AVG.

@@ -77,18 +77,11 @@
NEW_AVG
-

If he(1) gets 100 on the remaining plural(exam(1)), the sum of his(1) scores will be COUNT \cdot OLD_AVG + REMAINING \cdot 100 = COUNT * OLD_AVG + 100 * REMAINING.

-

His(1) overall average will then be COUNT * OLD_AVG + 100 * REMAINING \div COUNT + REMAINING = NEW_AVG.

+

If he(1) gets 100 on the remaining plural(exam(1)), the sum of his(1) scores will be COUNT \cdot OLD_AVG + REMAINING \cdot 100 = COUNT * OLD_AVG + 100 * REMAINING.

+

His(1) overall average will then be COUNT * OLD_AVG + 100 * REMAINING \div COUNT + REMAINING = NEW_AVG.

- -
-

-

-

-

-
28 exercises/direct_and_inverse_variation.html
 @@ -38,8 +38,8 @@

-

STATEMENT if V1 = k \cdot V2 for some constant k

-

V1 = MULTIPLIER \cdot V2 fits this pattern, with k = MULTIPLIER.

+

STATEMENT if V1 = k \cdot V2 for some constant k

+

V1 = MULTIPLIER \cdot V2 fits this pattern, with k = MULTIPLIER.

@@ -77,17 +77,17 @@

\frac{V1}{V2} = MULTIPLIER

-

If you divide each side of this expression by V2, you get \frac{V1}{V2} = k for some constant k.

-

\frac{V1}{V2} = MULTIPLIER fits this pattern, with k = MULTIPLIER.

+

If you divide each side of this expression by V2, you get \frac{V1}{V2} = k for some constant k.

+

\frac{V1}{V2} = MULTIPLIER fits this pattern, with k = MULTIPLIER.

MULTIPLIER \cdot V1 = V2

-

If you divide each side of this expression by k, you get \frac{1}{k} \cdot V1 = V2.

-

MULTIPLIER \cdot V1 = V2 fits this pattern, with k = MULTIPLIER_INVERSE.

+

If you divide each side of this expression by k, you get \frac{1}{k} \cdot V1 = V2.

+

MULTIPLIER \cdot V1 = V2 fits this pattern, with k = MULTIPLIER_INVERSE.

@@ -106,8 +106,8 @@

V1 = MULTIPLIER \cdot \frac{1}{V2}

-

STATEMENT if V1 = k \cdot \frac{1}{V2} for some constant k

-

V1 = MULTIPLIER \cdot \frac{1}{V2} fits this pattern, with k = MULTIPLIER.

+

STATEMENT if V1 = k \cdot \frac{1}{V2} for some constant k

+

V1 = MULTIPLIER \cdot \frac{1}{V2} fits this pattern, with k = MULTIPLIER.

@@ -148,8 +148,8 @@

V1 \cdot V2 = MULTIPLIER

-

If you multiply each side of this expression by V2, you get V1 \cdot V2 = k for some constant k.

-

V1 \cdot V2 = MULTIPLIER fits this pattern, with k = MULTIPLIER.

+

If you multiply each side of this expression by V2, you get V1 \cdot V2 = k for some constant k.

+

V1 \cdot V2 = MULTIPLIER fits this pattern, with k = MULTIPLIER.

@@ -161,16 +161,10 @@

If you divide each side of this expression by k, you get \frac{V1}{k} = \frac{1}{V2}.

Then you can take the inverse of each side to get \frac{k}{V1} = V2.

-

MULTIPLIER \cdot \frac{1}{V1} = V2 fits this pattern, with k = MULTIPLIER.

+

MULTIPLIER \cdot \frac{1}{V1} = V2 fits this pattern, with k = MULTIPLIER.

- -
-

-

-

-
30 exercises/equivalent_fractions.html
 @@ -22,9 +22,9 @@
D
-

To get the right numerator C, the left numerator A was multiplied by M.

-

To find the right denominator, multiply the left denominator by M as well.

-

B \times M = D

+

To get the right numerator C, the left numerator A was multiplied by M.

+

To find the right denominator, multiply the left denominator by M as well.

+

B \times M = D

@@ -34,9 +34,9 @@
C
-

To get the right denominator D, the left denominator B was multiplied by M.

-

To find the right numerator, multiply the left numerator by M as well.

-

A \times M = C

+

To get the right denominator D, the left denominator B was multiplied by M.

+

To find the right numerator, multiply the left numerator by M as well.

+

A \times M = C

@@ -46,9 +46,9 @@
B
-

To get the right numerator A, the left numerator C was divided by M.

-

To find the right denominator, divide the left denominator by M as well.

-

D \div M = B

+

To get the right numerator A, the left numerator C was divided by M.

+

To find the right denominator, divide the left denominator by M as well.

+

D \div M = B

@@ -58,18 +58,12 @@
A
-

To get the right denominator B, the left denominator D was divided by M.

-

To find the right numerator, divide the left numerator by M as well.

-

C \div M = A

+

To get the right denominator B, the left denominator D was divided by M.

+

To find the right numerator, divide the left numerator by M as well.

+

C \div M = A

- -
-

-

-

-
22 exercises/mean_median_and_mode.html
 @@ -72,12 +72,12 @@

MEAN

-

To find the mean, add the numbers and divide by the number of numbers.

-
+

To find the mean, add the numbers and divide by the number of numbers.

+
INTEGER_LIST

There are INTEGERS_COUNT numbers.

-

The mean is \frac{sum(INTEGERS)}{INTEGERS_COUNT}, +

The mean is \frac{sum(INTEGERS)}{INTEGERS_COUNT}, or MEAN.

@@ -92,17 +92,17 @@

MEDIAN

-
+

First, order the numbers, giving:

SORTED_LIST
-
+

Since we have 2 middle numbers, the median is the mean of those two numbers!

The median is the 'middle' number:

MEDIAN_LIST

The median is \frac{SORTED_INTS[ SORTED_INTS.length / 2 - 1 ] + SORTED_INTS[ SORTED_INTS.length / 2 ]}{2}.

-

So the median is MEDIAN.

+

So the median is MEDIAN.

@@ -115,19 +115,13 @@
-

The mode is the most frequent number.

-

There are more MODEs than any other number, so MODE is the mode.

+

The mode is the most frequent number.

+

There are more MODEs than any other number, so MODE is the mode.

MODE

- -
-

-

-

-
93 exercises/order_of_operations.html
 @@ -28,13 +28,13 @@

-

+

A + (B*C)

-

+

A + B*C

-

+

A+B*C

@@ -49,10 +49,10 @@

-

+

A + B*C

-

+

A+B*C

@@ -67,13 +67,13 @@

-

+

A \times (B+C)

-

+

A \times B+C

-

+

A*(B+C)

@@ -88,13 +88,13 @@

-

+

A + (B)

-

+

A + B

-

+

A+B

@@ -109,10 +109,10 @@

-

+

A + B

-

+

A+B

@@ -127,13 +127,13 @@

-

+

\frac{ (A*(B+C)) }{ ((B+C)) }

-

+

\frac{ (A*(B+C)) }{ B+C }

-

+

A

@@ -148,13 +148,13 @@

-

+

\frac{ (A*(B-C)) }{ ((B-C)) }

-

+

\frac{ (A*(B-C)) }{ B-C }

-

+

A

@@ -169,22 +169,22 @@

-

+

(A + (B - (C*D))) \times E

-

+

(A + ((B-(C*D)))) \times E

-

+

(A + (B-(C*D))) \times E

-

+

((A+(B-(C*D)))) \times E

-

+

(A+(B-(C*D))) \times E

-

+

A+(B-(C*D)))*E

@@ -199,19 +199,19 @@

-

+

A + (B - (C*D)) \times E

-

+

A + ((B-(C*D))) \times E

-

+

A + (B-(C*D)) \times E

-

+

A + ((B-(C*D))*E)

-

+

A+((B-(C*D))*E)

@@ -226,16 +226,16 @@

-

+

A - B \times C + D

-

+

A - (B*C) + D

-

+

(A-B*C) + D

-

+

A-B*C+D

@@ -250,16 +250,16 @@

-

+

A \times B + C \times D

-

+

(A*B) + C \times D

-

+

(A*B) + (C*D)

-

+

(A*B)+(C*D)

@@ -274,30 +274,21 @@

-

+

(A + (B*C)) - C \times E

-

+

(A+(B*C)) - C \times E

-

+

(A+(B*C)) - (D*E)

-

+

(A+B*C)-(D*E)

- -
-

-

-

-

-

-

-
35 exercises/probability_1.html
 @@ -49,10 +49,10 @@
-

There are RED + BLUE + GREEN = TOTAL MARBLEs in the CONTAINER.

-

There are CHOSEN_NUMBER CHOSEN_COLOR MARBLEs. +

There are RED + BLUE + GREEN = TOTAL MARBLEs in the CONTAINER.

+

There are CHOSEN_NUMBER CHOSEN_COLOR MARBLEs. That means TOTAL - CHOSEN_NUMBER = NUMER are not CHOSEN_COLOR.

-

The probability is \displaystyle fractionSimplification(NUMER, TOTAL).

+

The probability is \displaystyle fractionSimplification(NUMER, TOTAL).

@@ -105,10 +105,10 @@
-

When rolling a die, there are 6 possibilities: 1, 2, 3, 4, 5, and 6.

-

In this case, only 1 result is favorable: the number RESULT_POSSIBLE[0].

-

In this case, RESULT_COUNT results are favorable: toSentence(RESULT_POSSIBLE).

-

The probability is \displaystyle fractionSimplification(RESULT_COUNT, 6).

+

When rolling a die, there are 6 possibilities: 1, 2, 3, 4, 5, and 6.

+

In this case, only 1 result is favorable: the number RESULT_POSSIBLE[0].

+

In this case, RESULT_COUNT results are favorable: toSentence(RESULT_POSSIBLE).

+

The probability is \displaystyle fractionSimplification(RESULT_COUNT, 6).

@@ -187,10 +187,10 @@
-

There are (new Array(REPS)).join("2 \\cdot ")2 = 2^{REPS} = TWO_TO_REPS possibilities for the sequence of flips.

-

The possibilities are toSentence(ALL_SEQS).

-

There WANTED_COUNT == 1 ? "is only" : "are" plural(WANTED_COUNT, "favorable outcome"): toSentence(WANTED_LIST).

-

The probability is \displaystyle fractionSimplification(WANTED_COUNT, TWO_TO_REPS).

+

There are (new Array(REPS)).join("2 \\cdot ")2 = 2^{REPS} = TWO_TO_REPS possibilities for the sequence of flips.

+

The possibilities are toSentence(ALL_SEQS).

+

There WANTED_COUNT == 1 ? "is only" : "are" plural(WANTED_COUNT, "favorable outcome"): toSentence(WANTED_LIST).

+

The probability is \displaystyle fractionSimplification(WANTED_COUNT, TWO_TO_REPS).

@@ -238,19 +238,12 @@
-

There are POSSIBLE.length possibilities for the chosen number.
The possibilities are toSentence(POSSIBLE).

-

There WANTED_COUNT == 1 ? "is only" : "are" plural(WANTED_COUNT, "favorable outcome"): toSentence(WANTED_LIST).

-

The probability is \displaystyle fractionSimplification(WANTED_COUNT, POSSIBLE.length).

+

There are POSSIBLE.length possibilities for the chosen number.
The possibilities are toSentence(POSSIBLE).

+

There WANTED_COUNT == 1 ? "is only" : "are" plural(WANTED_COUNT, "favorable outcome"): toSentence(WANTED_LIST).

+

The probability is \displaystyle fractionSimplification(WANTED_COUNT, POSSIBLE.length).

- -
-

-

-

-

-
 @@ -63,8 +63,8 @@

-

To convert from degrees to radians, you multiply by \pi and then divide by 180^{\circ}.

-

+

To convert from degrees to radians, you multiply by \pi and then divide by 180^{\circ}.

+

@@ -79,8 +79,8 @@

-

To convert from degrees to radians, you multiply by \pi and then divide by 180^{\circ}.

-

+

To convert from degrees to radians, you multiply by \pi and then divide by 180^{\circ}.

+

@@ -95,8 +95,8 @@

COMMON_DEGREES°

-

To convert from radians to degrees, you multiply by 180^{\circ} and then divide by \pi.

-

+

To convert from radians to degrees, you multiply by 180^{\circ} and then divide by \pi.

+

@@ -111,8 +111,8 @@

round(NUM_DEGREES)°

-

To convert from radians to degrees, you multiply by 180^{\circ} and then divide by \pi.

-

+

To convert from radians to degrees, you multiply by 180^{\circ} and then divide by \pi.

+