SOLUTION: Mark is 10 years younger than Larry. Larry's age in 8 years will exceed twice Mark's age 3 years ago by 4 years. How old is each now?

Question 103611: Mark is 10 years younger than Larry. Larry's age in 8 years will exceed twice Mark's age 3 years ago by 4 years. How old is each now?

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let M = Mark's present age and L = Larry's present age.
From the problem description, you can write:
M = L-10 "Mark is 10 years younger than Larry"
(L+8) = 2(M-3)+4 "Larry's age in 8 years (L+8) will exceed twice Mark's age 3 years ago (2(M-3)) by 4 years (+4). Putting it all together, you have:
1) M = L-10 and
2) L+8 = 2(M-3)+4 Substitute the M from equation 1) here and solve for L.
L+8 = 2((L-10)-3)+4 Simplify and solve for L
L+8 = 2(L-13)+4
L+8 = 2L-26+4
L+8 = 2L-22 Subtract L from both sides.
8 = L-22 Add 22 to both sides.
30 = L
Larry's present age is 30
M = L-10
M = 30-10
M = 20
Mark's present age is 20
Check:
M = L-10
20 = 30-10
20 = 20 OK!
L+8 = 2(M-3)+4
30+8 = 2(20-3)+4
38 = 2(17)+4
38 = 34+4
38 = 38 OK!
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