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

The total number of hours worked between Ruby, Isaac, and Svetlana, hard-working friends with great names, is 126 and is equal to r + i + s. 126 = r + i + s. The relationships between Svetlana and Ruby's hours can be written as s = 4r. The relationship between Ruby and Isaac's hours can be written as r = i + 6, or i = r - 6. With these equations, we can return to the original equation and substitute for/ replace Svetlana and Isaac's hours so that the whole equation is in terms of r: 126 = (r) + (r-6) + (4r). Simplify this to 126 = 6r - 6 and then again to 132 = 6r and then at last to 22 = r, the number of hours that Ruby worked. Now returning to the other equations, we can plug in that r value to solve for i -- i = 22 - 6, or 16 hours for Isaac -- and for s -- s = 4(22), or a whopping 88 hours for Svetlana. We conclude that Isaac worked for 16 hours, Ruby worked for 22 hours, and Svetlana worked for 88 hours. 88 + 22 + 16 = 126 hours.