age problem

Say my age back then is x

So my moms back then was 7x

In 8 years, we add 15.

So 7x+15 and x+15

7x+15 is two times x+15

So 7x+15 equals 2x+30

5x=15

x=3

 

So back then your mother was 21.

 

Checking work

21+15=2(3+15)

(m-7) =  7(y-7)     m = mom   y = you      re-arrange to  y = 1/7 m + 6

(m+8) = 2(y+8)        or   y = 1/2 m - 4    substitute this value into the first equation

equate the two red equations       1/7 m + 6 = 1/2 m -4

                                                                10 = 5/14 m       so m = mom age now = 28        ( and you = 10 y/o)