a student makes a $10.25 purchase at the bookstore with $20 bill. The store has no bills and gives the change in quarters and fifty -cent pieces. There are 30 coings 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?___
Let h = # half dollars (50-cent pieces).
and q = # quarters.
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h+q=30
0.50*h + 0.25*q=20.00-10.25
Two equations. Two unknowns. Solve for h and q.
To solve this problem, we can set up a system of equations based on the given information. Let's use "Q" to represent the number of quarters and "F" to represent the number of fifty-cent pieces.
1. We know that the student made a $10.25 purchase with a $20 bill, so the change is $20 - $10.25 = $9.75.
2. Since the store only gives change in quarters and fifty-cent pieces, we can set up the first equation as:
0.25Q + 0.5F = $9.75
3. Additionally, we know that there are 30 coins in total, so we can set up the second equation as:
Q + F = 30
To solve this system of equations, we can use substitution or elimination method. Let's solve by elimination:
Multiply the second equation by -0.25 to make the coefficients of Q in both equations the same:
-0.25(Q + F) = -0.25(30)
-0.25Q - 0.25F = -7.5
Now, we can add this equation to the first equation:
0.25Q + 0.5F - 0.25Q - 0.25F = $9.75 - $7.5
0.25F = $2.25
To find the value of F, divide both sides of the equation by 0.25:
F = $2.25 / 0.25
F = 9
Now substitute the value of F into the second equation:
Q + 9 = 30
Q = 30 - 9
Q = 21
Therefore, there are 21 quarters and 9 fifty-cent pieces in the change.
To answer the specific questions:
- There are 21 quarters in the change.
- There are 9 fifty-cent pieces in the change.