Formulate the equation and solve the problem

Question

Steve is two years older than Marvin, Five years ago the sum of their ages was 10 years more than Steve's present age. How old was Marvin 5 years ago?

Answer 1

Let S = Steve's age now (yr)       M = Marvin's age now (yr)        M'  = Marvin's age 5 years ago = M - 5 = ?

 

1) S = M + 2

 

2) (S - 5) + (M - 5) = S + 10

 

Substitute eqn 1) into eqn 2) and solve for M:

 

(M + 2 - 5) + (M - 5)  = (M + 2) + 10        (combine like terms)

2*M - 8  = M + 12

M = 20

and

M' = M - 5 = 20 - 5 = 15 yrs old (Marvin's age 5 years ago)