Question

Tom's and Tim's ages add up to 21 years. In 3 years, Tom will be twice Tim’s age. How old are they now? A. Tom is 15, and Tim is 6. B. Tom is 12, and Tim is 9. C. Tom is 16, and Tim is 5. D. Tom is 14, and Tim is 7.

Answer 1

A. Tom is 15, and Tim is 6.

Explanation:

Method A: Use the choices to find the answer

Since you are given choices, you can try each choice until you see that one of the choices works.

Try choice A.

Ages now: 15 + 6 = 21 (This checks out.)

Ages in 3 years: Tom 15 + 3; Tim 6 + 3

(15 + 3)/(6 + 3) = 18/9 = 2 (This also checks out.)

The first choice works, so the answer is A.

Method B: Write an equation to solve the problem

Let Tom's age now = t.

Their ages add to 21, so Tim's age now is 21 - t.

In 3 years, Tom's age will be t + 3, and Tim's age will be 24 - t.

In 3 years, Tom's age will be twice Tim's age:

t + 3 = 2(24 - t)

t + 3 = 48 - 2t

3t = 45

t = 15

Tom's age is 15.

Tim's age is 21 - 15 = 6.

Tim's age is 6.

Answer 2

A. Tom is 15, and Tim is 6.

Explanation:

Method A: Use the choices to find the answer

Since you are given choices, you can try each choice until you see that one of the choices works.

Try choice A.

Ages now: 15 + 6 = 21 (This checks out.)

Ages in 3 years: Tom 15 + 3; Tim 6 + 3

(15 + 3)/(6 + 3) = 18/9 = 2 (This also checks out.)

The first choice works, so the answer is A.

Method B: Write an equation to solve the problem

Let Tom's age now = t.

Their ages add to 21, so Tim's age now is 21 - t.

In 3 years, Tom's age will be t + 3, and Tim's age will be 24 - t.

In 3 years, Tom's age will be twice Tim's age:

t + 3 = 2(24 - t)

t + 3 = 48 - 2t

3t = 45

t = 15

Tom's age is 15.

Tim's age is 21 - 15 = 6.

Tim's age is 6.