SOLUTION: There are 96 coins consisting of pennies,dimes, and quarters. the number of pennies is equal to the number of dimes and the total value is $22.05. How many coins of each tyoe are t
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Question 452610: There are 96 coins consisting of pennies,dimes, and quarters. the number of pennies is equal to the number of dimes and the total value is $22.05. How many coins of each tyoe are there? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! There are 96 coins consisting of pennies, dimes, and quarters.
p + d + q = 96
:
number of pennies is equal to the number of dimes
p = d
:
and the total value is $22.05.
.01p + .10d + .25 = 22.05
multiply by 100 to get rid of the decimals
p + 10d + 25q = 2205
:
Since d = p we can rewrite the 1st equation to:
2p + q = 96
q = (96-2p)
:
and
also rewrite the value equation to
11p + 25q = 2205
:
Replace q with (96-2p)
11p + 25(96-2p) = 2205
11p + 2400 - 50p = 2205
11p - 50p = 2205 - 2400
-39p = -195
p =
p = 5 pennies
then
d = 5 dimes
and
96 - 10 = 86 quarters
:
:
Check by finding the value
.01(5) + .10(5) + .25(86) =
.05 + .50 + 21.50 = 22.05; confirms our solutions of:
5 pennies, 5 dimes, 86 quarters
