Amy worked six hours more than Simon. Antonio worked four times as many hours as Amy. Combined, they all worked 126 hours, how many hours did each of them work?

Question

Amy worked six hours more than Simon. Antonio worked four times as many hours as Amy. Combined, they all worked 126 hours, how many hours did each of them work?

Answer 1

Let A = Amy's hours, S = Simon's hours and T = Tony's (Antonio) hours

Then, based on the sentences above:

A = S + 6

T = 4A or T = 4(S + 6) or S = T/4 - 6

A + S + T = 126

Substituting: T/4 + T/4 -6 + T = 126 or T + T/2 = 132 = 3T/2 So

T = 2/3(132) = 88

A = T/4 = 22

S = A - 6 = 16