SOLUTION: Audrey has 28 dimes and quarters in her piggy bank with a total value of $4.75. How many of the coins are dimes and how many are quarters?

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Question 149572: Audrey has 28 dimes and quarters in her piggy bank with a total value of $4.75. How many of the coins are dimes and how many are quarters?
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call dimes, D, and quarters, Q.
1.D%2BQ=28 Total number of coins.
2.0.10%2AD%2B0.25%2AQ=4.75 Total value of coins.
Let's multiply equation 2 by 100 to get rid of decimals.
1.D%2BQ=28
2.10D%2B25Q=475
Use eq. 1 to solve for D and a function of Q.
1.D%2BQ=28
D=28-Q
Now substitute this expression for D in eq. 2,
2.10D%2B25Q=475
10%2828-Q%29%2B25Q=475
Solve for Q.
280-10Q%2B25Q=475
280%2B15Q=475
15Q=195
Q=13
Use eq.1 to solve for D.
D=28-Q
D=28-13
D=15
Audrey has 15 dimes and 13 quarters.