Question 119992
Mrs. Brooks lacks 7 years from being five times as old as her son. Six years from now she will lack 3 years from being three times as old as her son is then. Find each of their ages. 
:
B = Brooks present age; S = Son's present age
:
Mrs. Brooks lacks 7 years from being five times as old as her son.
(B+7) = 5S
B = 5S - 7
:
 Six years from now she will lack 3 years from being three times as old as her son is then.
That translates to: 
B + 6 + 3 = 3(S + 6)
B + 9 = 3S + 18
B = 3S + 18 - 9
B = 3s + 9
:
Find each of their ages.
Substitute (5S-7) for B and find S
5S - 7 = 3S + 9
5S = 3S + 9 + 7
5S - 3S = 16
S = 16/2
S = 8 yr is the son
:
B = 5S - 7
B = 40 - 7
B = 33 yrs is the Mom (Brooks)
:
Check solutions the statement:
Six years from now she will lack 3 years from being three times as old as her son is then. 
33 + 6 + 3 = 3(8 + 6)
42 = 3 * 14; confirms our solution
:
:
I'm not sure what you did, You seemed to start out right
Hope this helps you.