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?
How many quarters are there in the change___?
How many fifty-cent pieces are there in the change___?
20.00 - 9.25 = 10.75
25 q + 50 f = 1075
q + f = 30
q + 2 f = 43 divided top one by 25
q + 1 f = 30
------------ subtract
f = 13
you can do it now
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume that the number of quarters is represented by the variable 'q', and the number of fifty-cent pieces is represented by the variable 'f'.
We know that the total number of coins is 30, so our first equation is:
q + f = 30
We also know that the total value of the coins is equal to the amount of change given. In this case, the change is $20 - $9.25 = $10.75. Since we are given that the store only gives change in quarters (25 cents) and fifty-cent pieces, we can set up our second equation as:
0.25q + 0.50f = 10.75
Now we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of 'q' and 'f'.
One way to solve this system of equations is by substitution:
1. Solve the first equation for 'q' in terms of 'f':
q = 30 - f
2. Substitute the expression for 'q' into the second equation:
0.25(30 - f) + 0.50f = 10.75
3. Simplify and solve for 'f':
7.5 - 0.25f + 0.50f = 10.75
0.25f = 10.75 - 7.5
0.25f = 3.25
f = 3.25 / 0.25
f = 13
Now that we know the value of 'f' (the number of fifty-cent pieces), we can substitute it back into the first equation to find the value of 'q':
q + 13 = 30
q = 30 - 13
q = 17
Therefore, there are 17 quarters and 13 fifty-cent pieces in the change.