Total number of hours each worked

Question

One month, Ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 126 hours. Find the number of hours each person worked.

Answer 1

Let h = number of hours worked by Isaac.

 

Then, h + 6 = number of hours worked by Ruby

 

        4(h + 6) = number of hours worked by Svetlana

 

Therefore, total number of hours worked can be written as:

 

h + (h + 6) + 4(h + 6) = 126

 

h + h + 6 +4h + 24 = 126

 

Combining like terms yields:

 

6h + 30 = 126

 

6h = 96 (Subtract 30 from each side)

 

h = 96/6

 

h = 16

 

Therefore, Isaac worked 16 hours; Ruby worked 16 + 6 =22 hours; Svetlana worked 4(22) = 88 hours.

 

Check the solution for correctness: 16 + 22 + 88 = 126

 

Answer 2

R = # hours Ruby worked

I = # hours Isaac worked

S = # hours Svetlana worked

 

R = I + 6    Ruby worked 6 hours more than Isaac

S = 4R = 4(I+6) = 4I + 24    Svetlana worked 4 times as many hours as Ruby

I + R + S = 126

 

I + I+6 + 4I+24 = 126

6I + 30 = 126

6I = 96

I = 16

 

R = I+6 = 22

 

S = 4R = 88

 

Isaac worked 16 hours

Ruby worked 22 hours

Svetlana worked 88 hours