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.

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.