###### Exercise 4

The fuel inside model rocket motors is a black powder mixture that ideally consists of 60% charcoal, 30% potassium nitrate, and 10% sulfur by weight.

Suppose you work at a company that makes model rocket motors. When you come into work one morning, you learn that yesterday's first shift made a perfect batch of fuel. The second shift, however, misread the recipe and used 50% charcoal, 20% potassium nitrate and 30% sulfur. Then the two batches were mixed together. A chemical analysis shows that there are 100.3 pounds of charcoal in the mixture and 46.9 pounds of potassium nitrate.

Assuming the first shift produced \(x\) pounds of fuel and the second \(y\) pounds, set up a linear system in terms of \(x\) and \(y\text{.}\) How many pounds of fuel did the first shift produce and how many did the second shift produce?

How much sulfur would you expect to find in the mixture?