A student makes a 9.25 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?
The student is going to get $10.75 of change ($20-$9.25=$10.75) and we get Quarters and Fifty-cent pieces. I'll assign Q for the number of quarters and F for the number of fifty-cent pieces.
We know two things:
Now let's solve for Q and F:
Before I distribute this out, I'm going to multiply both sides by 4 to get rid of the decimals:
Does this work? Let's check: