Let: A = Allen's age NOW
Let: B = Ben's age NOW
Then: A-7 = Allen's age 7 years ago
And: B-7 = Ben's age 7 years ago.
Also: one-half as old as Ben was then = (B-7)
And: 16 years more than one- half as old as Ben was then =
(B-7)+16
" The sum of Allan and Ben's age is 45.
A + B = 45
Seven years ago, Allan was 16 years more than one- half as old as Ben was then.
A-7 = (B-7)+16
So the system of equations is
Simplify the second equation, first by multiplying
both sides by 2:
Now solve the system of equations:
Edwin