SOLUTION: Maggie makes a $9.25 purchase at a bookstore in Reno with a $20 bill. The store has no bills and gives her the change in quarters and fifty-cent pieces. There are 30 coins in all.

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Question 176729: Maggie makes a $9.25 purchase at a bookstore in Reno with a $20 bill. The store has no bills and gives her the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?

please help me! thank you!!
Found 2 solutions by solver91311, checkley75:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The number of quarters: q

The number of 50c pieces: f

Given: q+%2B+f+=+30

The value of each quarter is 25 cents, so the value of all her quarters is 25q in cents.

Similarly the value of all her 50c pieces is 50f

The total value of her change is 20+-+9.25+=+10.75 dollars which is the same as 1075 cents. The value of the quarters plus the value of the 50c pieces must equal the total value of the change, so:

25q+%2B+50f+=+1075

Solve the first equation for q: q+%2B+f+=+30 → q+=+30+-+f.

Substitute this expression for q into the second equation:

cartoon%2825%2Ared%28q%29+%2B+50f+=+1075%2C+25%2Ared%28%2830+-+f%29%29+%2B+50f+=+1075%29

Solve for f

25%2830+-+f%29+%2B+50f+=+1075

750+-+25f+%2B+50f+=+1075

25f+=+325

f+=+13

So there were 13 half-dollars, and therefore 30+-+13+=+17 quarters.

Check:
17+%2A+.25+=+4.25

13+%2A+.50+=+6.50

4.25+%2B+6.50+=+10.75 Checks.

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
20-9.25=10.75 is the amount of change.
.25x+.5(30-x)=10.75
.25x+15-.5x=10.75
-.25x=10.75-15
-.25x=-4.25
x=4.25/-.25
x=17 number of quarters.
30-17=13 number of half dollares.
Proof:
.25*17+.50*13=10.75
4.25+6.50=10.75
10.75=10.75