SOLUTION: a box contains 34 coins, consisting of pennies dimes and quaters. the number of pennies is equal to the number of dimes and the total value is $3.82. how many of each denomination

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Question 498970: a box contains 34 coins, consisting of pennies dimes and quaters. the number of pennies is equal to the number of dimes and the total value is $3.82. how many of each denomination of coins do you have
Found 2 solutions by chessace, htmentor:
Answer by chessace(471) (Show Source):
You can put this solution on YOUR website!
2p+q=34
11p+25q=382
11p+25(34-2p)=382
39p=25*34-382
p=468/39=12=d
q=10

Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website!
a box contains 34 coins, consisting of pennies dimes and quaters. the number of pennies is equal to the number of dimes and the total value is $3.82. how many of each denomination of coins do you have?
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Let p = the number of pennies and dimes
Let q = the number of quarters
Given: total number of coins = 34; total value = $3.82
For the total number of coins we can write
p + p + q = 34
2p + q = 34 [1]
And for the total amount we can write
p + 10p + 25q = 382 [2]
Solve for q in [1]:
q = 34 - 2p
Substitute into [2]:
p + 10p + 25(34 - 2p) = 382
Simplify and solve:
11p - 50p = 382 - 850
-39p = -468
p = 12
Therefore q = 34 - 2*12 = 10
So the number of pennies and dimes = 12, the number of quarters = 10