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?

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

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