Answer:
Simon: 55 hours
Alvin: 70 hours
Theodore: 159 hours
Total: 284 hours
Step-by-step explanation:
Let A, T, and S stand for the hours worked by Alvin, Simon, and Theodore.
We are told that:
A = S + 15,
T = 3S - 6
and
A + S + T = 284
Note that the first two equations state the value of A and T in terms of S. Let's use them in the third equation, so that we'll have only one unknow:
A + S + T = 284
(S + 15) + S + (3S - 6) = 284
5S + 9 = 284
S = 55
Now use this value of S in the first two equations to find A and T:
A = S + 15
A = 55 + 15
A = 70
T = 3S - 6
T = 3*55 - 6
T = 159
(55 + 70 + 159) = 284
