Jemma is three times as old as Angie. Five years from now the sum of their ages will be 34 years. What are their present ages?

Answer: Angie = 6, Jemma = 18

Step-by-step explanation:

Let x represent the current age of Angie

Current Age Age 5 years from now

Angie: x x + 5

Jemma: 3x 3x + 5

5 years from now the sum of their ages is 34

(x + 5) + (3x + 5) = 34

4x + 10 = 34

4x = 24

x = 6

Angle's current age is x = 6

Jemma's current age is 3x = 3 (6) = 18

Answer: Angie is 6 years and Jemma is 18 years

Step-by-step explanation:

Let Jemma'a age be J and Angie's be A.

Then:

J = 3A ... Equation 1

Five years from now, Jemma will be J+5 years and Angie will be A+5 years.

That is:

J+5+A+5 = 34

Re arranging we have:

J + A+10 = 34

subtract 10 from both sides

J+A = 24 ... Equation 2

recall that J=3A

Substitute J = 3A into equation 2, then we have:

3A + A = 24

4A = 24

divide through by 4

A = 6

substitute A = 6 into equation 1, we have

J = 3 (6)

J = 18

Therefore:

Angie is 6 years and Jemma is 18 years