SOLUTION: A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the
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Question 105059: A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the number of coins of each type in the machine. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! :
A change machine contains nickels, dimes, and quarters.
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Just write an equation for each statement:
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"There are 75 coins in the machine,"
n + d + q = 75
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"the value of the coins is $7.25."
.05n + .10n + .25q = 7.25
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" There are 5 times as many nickels as dimes."
n = 5d
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Find the number of coins of each type in the machine.
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Substitute 5d for n in the 1st equation:
5d + d + q = 75
6d + q = 75
q = (75-6d); use this for substitution later
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Substitute 5d for n in the 2nd equation:
.05(5d) + .10d + .25q = 7.25
.25d + .10d + .25q = 7.25
.35d + .25q = 7.25
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In the above equation substitute (75-6d) for q:
.35d + .25(75-6d) = 7.25
.35d + 18.75 - 1.5d = 7.25
.35d - 1.5d = 7.25 - 18.75
-1.15d = -11.5
d = -11.5/-1.15
d = +10 dimes
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Find the nickels from n = 5d
n = 5(10)
n = 50 nickels
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Find q using the 1st equation:
50 + 10 + q = 75
60 + q = 75
q = 75 - 60
q = 15 quarters
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Check our solutions on the 2nd equation:.
.05(50) + .10(10) + .25(15) =
2.50 + 1.00 + 3.75 = 7.25; confirms our solutions
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Did this makes sense to you? A lot of steps but each one is logical and simple.
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