One month, Ruby worked 8 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked \(96\) hours. Find the number of hours each person worked.
+2666 Write as a system of 3 equations:
\(r = 8+i\) (1)
\(s = 4r\) (2)
\(i+r+s=96\) (3)
Rearrange (1) so \(i\) is the independent variable: \(i = r - 8\)
Now, substitute i and s in terms of r: \(r + 4r + r-8 =96\)
Simplify: \(6r - 8 = 96\)
Add 8 to both sides: \(6r = 104\)
Divide by 6: \(r = 17 {1 \over 3}\)
Now substitute \(r\) into (1) and solve for \(i\): \(17 {1 \over3} = 8 + i\)
Subtract 8 from both sides: \(i = 9 {1 \over3}\)
Now substitute \(r\) into (2) and solve for \(s\): \(4 \times 17 {1 \over 3} = s\)
Simplify: \(s = 69 {1 \over 3}\)
+2666 Sorry, this site is too addicting...
Also, it's not about getting here "first"... It's about helping people learn.
