Question

Two years ago, Rita was three times older than Cheryl. In 3 years, Rita will be twice older than Cheryl. How old are the girls now?

Answer 1

Answer:

Cheryl's age = x = 7 years

Rita's age = y = 17 years

Step-by-step explanation:

Let

Cheryl's age = x

Rita's age = y

Two years ago, Rita was three times older than Cheryl

(y - 2) = 3(x - 2)

y - 2 = 3x - 6

y = 3x - 6 + 2

= 3x - 4

y = 3x - 4

In 3 years, Rita will be twice older than Cheryl

(y + 3) = 2(x + 3)

y + 3 = 2x + 6

y = 2x + 6 - 3

= 2x + 3

y = 2x + 3

Equate both equations

3x - 4 = 2x + 3

Collect like terms

3x - 2x = 3 + 4

x = 7 years

Substitute x = 7 into

y = 2x + 3

= 2(7) + 3

= 14 + 3

= 17

y = 17 years

Cheryl's age = x = 7 years

Rita's age = y = 17 years