Question 131381: 1. Samantha has a total of one hundred forty-one pennies, nickels and quarters. She has a total of $15.17. She has fifteen more quarters than pennies and fifteen fewer quarters than nickels. How many of each coin does she have?
2. Jordan has a total of one hundred thirty nickels, dimes and quarters. He has three and a half times as many nickels as dimes, and one-half as many quarters as dimes. How much money does he have?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Samantha has a total of one hundred forty-one pennies, nickels and quarters. She has a total of $15.17. She has fifteen more quarters than pennies and fifteen fewer quarters than nickels. How many of each coin does she have?
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Let # of pennies be "x" ; value of these is x cents
# of quarters is "x+15" ;value is 25(x+15)=25x+375 cents
# of nickels is "x+15+15" ; value is 5(x+30)=5x+150 cents
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EQUATION:
value + value + value = 1517 cents
x + 25x+375 + 5x + 150 = 1517
31x = 992
x = 32 (# of pennies)
x+15 = 47 (# of quarters)
x+30 = 62 (# of nickels)
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2. Jordan has a total of one hundred thirty nickels, dimes and quarters. He has three and a half times as many nickels as dimes, and one-half as many quarters as dimes. How much money does he have?
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Let number of dimes be "x" ; value is 10x cents
# of nickels is (7/2)x ; value is 5(7/2)x = (35/2)x
# of quarters is x/2 ; value is 25(x/2) = (25/2)x
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EQUATION:
# + # + # = 130
x + (7/2)x + (1/2)x = 130
2x + 7x + x = 260
10x = 260
x = 26 (# of dimes; value is 260 cents)
(7/2)x = 91 (# of nickels ; value is 455 cents)
(x/2) = 13 (# of quarters ; value is 425 cents)
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Value of the coins is 260 + 455 + 425 cents = $11.40
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Cheers,
Stan H.
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