SOLUTION: Audrey has 35 dimes and quarters in her piggy bank with a total value of $6.95. How many coins are dimes and how many are quarters?

Question 148920: Audrey has 35 dimes and quarters in her piggy bank with a total value of $6.95. How many coins are dimes and how many are quarters?
Found 2 solutions by nabla, mangopeeler07:
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
Form this system of equations from the given:
d+q=35 (number of dimes plus number of quarters =35)
.1d+.25q=6.95 (number of dimes times their worth plus number of quarters times their worth= 6.95)

So, we can solve this a few ways. I will first multiply the second equation by 100.
d+q=35
10d+25q=695

Now, multiply the first equation by -10.
-10d-10q=-350
10d+25q=695
Now, add the two equations.
15q=345
q=23
If q=23,
d=35-23=12

So Audrey has 23 quarters and 12 dimes.
Check:
23(.25)+1.2=5.75+1.2=6.95.
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
d=# dimes
q=# quarters
coefficient=value of coin in cents

10d+25q=695
d+q=35

Solve for d in the second equation:
d=35-q

Plug that into the first equation:
10(35-q)+25q=695

Distribute:
350-10q+25q=695

Combine like terms:
350+15q=695

Subtract 350 from both sides
15q=345

Divide by 15
q=23

Plug that into the second equation:
d+23=35
d=12

23 quarters
12 dimes
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