Question

Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's & Jim's age. Find the present age of each one of them.

Carla: ________ Jim: ________ Peter: _______

Answer 1

Answer: Carla: 5, Jim: 6, Peter: 9

Explanation:

Let c be Carla's age, j be Jim's age, and p be Peter's age.

We can set up equations.

We already know that c = 5

j + 13 = p

p-1 = 2(c - 1 + j - 1)

Combine like terms:

p - 1 = 2(c + j - 2)

Distribute:

p - 1 = 2c + 2j - 4

p + 3 = 2c + 2j

We can plug in the value of 5 for c.

p + 3 = 10 + 2j

2j + 7 = p

We can plug in j + 13 for p.

2j + 7 = j + 13

Combine like terms:

j = 6

Therefore, p = 6 + 13 = 9