SOLUTION: Paul has 30 coins in dimes and quarters. Their total value is $4.50. Find the number of each coin.

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Question 225098: Paul has 30 coins in dimes and quarters. Their total value is $4.50. Find the number of each coin.
Answer by LtAurora(115) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, set up the two given equations:
Q%2BD=30
.25Q%2B.1D=4.50
Solve the first one for one of the variables:
Q=30-D
Plug this into the second equation:
.25%2830-D%29%2B.1D=4.5
Simplify:
30%2F4-.25D%2B.1D=4.5
Combine like terms:
30%2F4-.15D=4.5
Subtract the 30%2F4 from both sides:
-.15D=-3
Divide both sides by -.15:
D=20
So, we have 20 dimes.
Since we know that Q=30-D=30-20=10
So, 10 quarters.
Checking our work, 20 dimes = $2 and 10 quarters = $2.5. The sum of those two gives us $4.5, so we're correct. Yay!
:-)