Solve.
-The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal and Cal is 1 year younger than Ben. Which of these people were teenagers 7 years ago?
A)Art, Ben, and Cal
B)Ben
C)Art and Ben
D)Art

Question

Quizplus · Accepted Answer

Let's start by assigning variables to their ages. Let A = Art's age, B = Ben's age, and C = Cal's age. We know that:

A + B + C = 59
A = C + 1
C = B - 1

Using the second and third equations, we can substitute for A and C in the first equation:

(C + 1) + B + (B - 1) = 59
2B = 59

This gives us Ben's current age: B = 29. Therefore, Art's current age is A = 30 and Cal's current age is C = 28.

To find out who was a teenager 7 years ago, we need to subtract 7 from each of their ages:

A - 7 = 23
B - 7 = 22
C - 7 = 21

Therefore, Art and Ben were teenagers 7 years ago, but not Cal. So, the correct answer is C.

Solve. -The Sum of the Ages of Art, Ben, and Cal