Question 87978: there are 155 coin nickels,dimes, quarters= 24.95 the number of dimes is t more than twice the number of nickels
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write an equation for each phrase:
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"there are 155 coin nickels,dimes, quarters"
n + d + q = 155
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"nickels, dimes, quarters = 24.95 "
.05n + .10d + .25q = 24.95
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"the number of dimes is two more than twice the number of nickels"
d = 2n + 2
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Replace (2n+2) for d in the coin# and $amt equations:
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1st equation:
n + (2n+2) + q = 155
3n + 2 + q = 155
3n + q = 155 - 2
3n + q = 153
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2nd Equation
.05n + .10(2n+2) + .25q = 24.95
.05n + .2n + .2 + .25q = 24.95
.25n + .25q = 24.95 - .2
.25n + .25q = 24.75
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Multiply the 2nd equation by 4 and subtract from the 1st equation
3n + q = 153
1n + q = 99
-------------subtracting eliminates q
2n = 54
n = 54/2
n = 27 nickels
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Given d = 2n+2
d = 2(27) + 2
d = 56 dimes
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Find q using the coin# equation
27 + 56 + q = 155
q = 155 - 83
q = 72 quarters
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Check solution using $amt equation:
.05(27) + .10(56) + .25(72) = 24.95
:
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