# Khan/khan-exercises

returned alternatives to directory

1 parent f158d2b commit da9d4f3c6dd8f50e902fcaf992b37523a5c1a391 Helpsypoo committed Feb 14, 2013
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355 exercises/age_word_problems_alternative.html
 @@ -0,0 +1,355 @@ + + + + + Age word problems + + + +
+
+
+
+ randRange(3, 5) + randRange(2, 20) + randRange(1, 10) * (C - 1) +
+ +
+

+ {person(1) is A years older than person(2)|person(2) is A years younger than person(1)}. + {For the last {four|3|two} years, person(1) and person(2) have been going to the same school.|person(1) and person(2) first met 3 years ago.|} + Cardinal(B) years ago, person(1) was C times {as old as|older than} person(2).

+ +

How old is person(1) now?

+
+
(C * (B + A) - B) / (C - 1)
+ +
+

We can use the given information to write down two equations that describe the ages of person(1) and person(2).

+

Let person(1)'s current age be personVar(1) and person(2)'s current age be personVar(2).

+
+

The information in the first sentence can be expressed in the following equation:

+
+

personVar(1) = personVar(2) + A

+
+
+ $(".first").addClass("hint_blue"); + + + Cardinal(B) years ago, person(1) was personVar(1) - B years old, and person(2) was personVar(2) - B years old. + + The information in the second sentence can be expressed in the following equation: + + personVar(1) - B = C(personVar(2) - B) + + +$(".second").addClass("hint_red"); +
+
+

Now we have two independent equations, and we can solve for our two unknowns.

+

Because we are looking for personVar(1), it might be easiest to solve our first equation for personVar(2) and substitute it into our second equation.

+
+

Solving our first equation for personVar(2), we get: personVar(2) = personVar(1) - A. Substituting this into our second equation, we get the equation:

+
+

personVar(1) - B = C((personVar(1) - A) - B)

+
+

which combines the information about personVar(1) from both of our original equations.

+
+

Simplifying the right side of this equation, we get: personVar(1) - B = CpersonVar(1) - C * (A + B).

+

Solving for personVar(1), we get: C - 1 personVar(1) = C * (A + B) - B.

+

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

+
+
+ +
+
+

person(1) is A years older than + person(2). Cardinal(B) years ago, person(1) + was C times as old as person(2).

+ +

How old is person(2) now?

+
+
(A - B + C * B) / (C - 1)
+ +
+

We can use the given information to write down two equations that describe the ages of person(1) and person(2).

+

Let person(1)'s current age be personVar(1) and person(2)'s current age be personVar(2).

+
+

The information in the first sentence can be expressed in the following equation:

+
+

personVar(1) = personVar(2) + A

+
+
+ $(".first").addClass("hint_blue"); + + + Cardinal(B) years ago, person(1) was personVar(1) - B years old, and person(2) was personVar(2) - B years old. + + The information in the second sentence can be expressed in the following equation: + + personVar(1) - B = C(personVar(2) - B) + + +$(".second").addClass("hint_red"); +
+
+

Now we have two independent equations, and we can solve for our two unknowns.

+

Because we are looking for personVar(2), it might be easiest to use our first equation for personVar(1) and substitute it into our second equation.

+
+

Our first equation is: personVar(1) = personVar(2) + A. Substituting this into our second equation, we get the equation:

+
+

(personVar(2) + A) - B = C(personVar(2) - B)

+
+

which combines the information about personVar(2) from both of our original equations.

+
+

Simplifying both sides of this equation, we get: personVar(2) + A - B = C personVar(2) - C * B.

+

Solving for personVar(2), we get: C - 1 personVar(2) = A - B + C * B.

+

personVar(2) = (A - B + C * B) / (C - 1).

+
+
+ +
+
+ randRange(3, 5) + randRange(2, 10) * (C - 1) +
+ +
+

person(1) is C times as old as + person(2) and is also A + years older than person(2).

+ +

How old is person(1)?

+
+
A * C / (C - 1)
+ +
+

We can use the given information to write down two equations that describe the ages of person(1) and person(2).

+

Let person(1)'s current age be personVar(1) and person(2)'s current age be personVar(2).

+
+
+

personVar(1) = CpersonVar(2)

+
+
+

personVar(1) = personVar(2) + A

+
+
+ $(".first").addClass("hint_blue"); +$(".second").addClass("hint_red"); +
+
+

Now we have two independent equations, and we can solve for our two unknowns.

+

One way to solve for personVar(1) is to solve the second equation for personVar(2) and substitute that value into the first equation.

+
+

Solving our second equation for personVar(2), we get: personVar(2) = personVar(1) - A. Substituting this into our first equation, we get the equation:

+
+

personVar(1) = C(personVar(1) - A)

+
+

which combines the information about personVar(1) from both of our original equations.

+
+

Simplifying the right side of this equation, we get: personVar(1) = CpersonVar(1) - C * A.

+

Solving for personVar(1), we get: C - 1 personVar(1) = A * C.

+

personVar(1) = A * C / (C - 1).

+
+
+ +
+
+

person(1) is C times as old as + person(2) and is also A + years older than person(2).

+ +

How old is person(2)?

+
+
A / (C - 1)
+ +
+

We can use the given information to write down two equations that describe the ages of person(1) and person(2).

+

Let person(1)'s current age be personVar(1) and person(2)'s current age be personVar(2).

+
+
+

personVar(1) = CpersonVar(2)

+
+
+

personVar(1) = personVar(2) + A

+
+
+ $(".first").addClass("hint_blue"); +$(".second").addClass("hint_red"); +
+
+

Now we have two independent equations, and we can solve for our two unknowns.

+

Since we are looking for personVar(2), and both of our equations have personVar(1) alone on one side, this is a convenient time to use elimination.

+
+

Subtracting the second equation from the first equation, we get:

+
+

0 = CpersonVar(2) - (personVar(2) + A)

+
+

which combines the information about personVar(2) from both of our original equations.

+
+

Solving for personVar(2), we get: C - 1 personVar(2) = A.

+

personVar(2) = A / (C - 1).

+
+
+ +
+
+ randRange(2, 5) + randRange(A + 2, 9) + randRange(2, 7) * (C - A) +
+ +
+

person(1) is A times as old as person(2). Cardinal(B) years ago, person(1) was C times as old as person(2).

+ +

How old is person(1) now?

+
+
A * B * (C - 1) / (C - A)
+ +
+

We can use the given information to write down two equations that describe the ages of person(1) and person(2).

+

Let person(1)'s current age be personVar(1) and person(2)'s current age be personVar(2).

+
+

The information in the first sentence can be expressed in the following equation:

+
+

personVar(1) = ApersonVar(2)

+
+
+ $(".first").addClass("hint_blue"); + + + Cardinal(B) years ago, person(1) was personVar(1) - B years old, and person(2) was personVar(2) - B years old. + + The information in the second sentence can be expressed in the following equation: + + personVar(1) - B = C(personVar(2) - B) + + +$(".second").addClass("hint_red"); +
+
+

Now we have two independent equations, and we can solve for our two unknowns.

+

Because we are looking for personVar(1), it might be easiest to solve our first equation for personVar(2) and substitute it into our second equation.

+
+

Solving our first equation for personVar(2), we get: personVar(2) = personVar(1) / A. Substituting this into our second equation, we get:

+
+

personVar(1) - B = C( (personVar(1) / A) - B)

+
+

which combines the information about personVar(1) from both of our original equations.

+
+

Simplifying the right side of this equation, we get: personVar(1) - B = fractionReduce(C, A) personVar(1) - C * B.

+

Solving for personVar(1), we get: fractionReduce(C - A, A) personVar(1) = B * (C - 1).

+

personVar(1) = fractionReduce(A, C - A) \cdot B * (C - 1) = A * B * (C - 1) / (C - A).

+
+
+ +
+
+

person(1) is A times as old as person(2). Cardinal(B) years ago, person(1) was C times as old as person(2).

+ +

How old is person(2) now?

+
+
B * (C - 1) / (C - A)
+ +
+

We can use the given information to write down two equations that describe the ages of person(1) and person(2).

+

Let person(1)'s current age be personVar(1) and person(2)'s current age be personVar(2).

+
+

The information in the first sentence can be expressed in the following equation:

+
+

personVar(1) = ApersonVar(2)

+
+
+ $(".first").addClass("hint_blue"); + + + Cardinal(B) years ago, person(1) was personVar(1) - B years old, and person(2) was personVar(2) - B years old. + + The information in the second sentence can be expressed in the following equation: + + personVar(1) - B = C(personVar(2) - B) + + +$(".second").addClass("hint_red"); +
+
+

Now we have two independent equations, and we can solve for our two unknowns.

+

Because we are looking for personVar(2), it might be easiest to use our first equation for personVar(1) and substitute it into our second equation.

+
+

Our first equation is: personVar(1) = ApersonVar(2). Substituting this into our second equation, we get:

+
+

ApersonVar(2) - B = C(personVar(2) - B)

+
+

which combines the information about personVar(2) from both of our original equations.

+
+

Simplifying the right side of this equation, we get: A personVar(2) - B = C personVar(2) - B * C.

+

Solving for personVar(2), we get: C - A personVar(2) = B * (C - 1). +

personVar(2) = B * (C - 1) / (C - A).

+
+
+ +
+
+ randRange(3, 20) + randRange(7, 24) * (A - 1) +
+ +
+

In B years, person(1) will be A times as old as he(1) is right now.

+ +

How old is he(1) right now?

+
+
B / (A - 1)
+ +
+

We can use the given information to write down an equation about person(1)'s age.

+

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.

+
+

Writing this information as an equation, we get:

+
+

personVar(1) + B = A personVar(1)

+
+
+

Solving for personVar(1), we get: A - 1 personVar(1) = B.

+

personVar(1) = B / (A - 1).

+
+
+ +
+
+ randRange(3, 5) + randRange(1, 10) * (C - 1) + randRange(C * B + 1, 15) * (C - 1) +
+ +
+

person(1) is A years old and person(2) is B years old.

+ +

How many years will it take until person(1) is only C times as old as person(2)?

+
+
(A - B * C) / (C - 1)
+ +
+

We can use the given information to write down an equation about how many years it will take.

+

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).

+
+

Writing this information as an equation, we get:

+
+

A + y = C (B + y)

+
+
+

Simplifying the right side of this equation, we get: A + y = C * B + C y.

+

Solving for y, we get: C - 1 y = A - C * B.

+

y = (A - C * B) / (C - 1).

+
+
+
+
+ + +