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.|} CardinalThrough20(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");

CardinalThrough20(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). CardinalThrough20(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");

CardinalThrough20(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). CardinalThrough20(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");

CardinalThrough20(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). CardinalThrough20(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");

CardinalThrough20(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 is right now.

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

How old is he right now?

How old is she 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 will be personVar(1) + B years old.

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

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

At that time, she 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).