SOLUTION: 1. 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 mo

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: 1. 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 mo      Log On

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Question 87411: 1. 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?

2. Austin has nickels, dimes and quarters. He has a total of $17.65. He has eleven fewer quarters than nickels and six times as many dimes as quarters. How many of each coin does he have?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
n = number of nickels
d = number of dimes
q = number of quarters
n+%2B+d+%2B+q+=+130
n+=+3.5q
q+=+.5d
3.5d+%2B+d+%2B+.5d+=+130
5d+=+130
d+=+26
n+=+3.5%2A26
n+=+91
q+=+.5%2A26
q+=+13
To find how much money he has, find 5n, 10d, and 25q
91%2A5+%2B+26%2A10+%2B+13%2A25
455+%2B+260+%2B+325
The answer is 1040 cents, or $10.40
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In this case,
n = number of nickels
d = number of dimes
q = number of quarters
as before, but what is known is how much money he has
and not the total number of coins
10d+%2B+5n+%2B+25q+=+1765 (in cents)
q+=+n+-+11
d+=+6q
Solve the 1st equation for n
n+=+q+%2B+11
Now find d and n in 10d+%2B+5n+%2B+25q+=+1765 in terms of q
10%2A6q+%2B+5%28q+%2B+11%29+%2B+25q+=+1765
60q+%2B+5q+%2B+25q+%2B+55+=+1765
90q+=+1710
q+=+19
d+=+6q
d+=+114
n+=+q+%2B+11
n+=+19+%2B+11
n+=+30
The answer is 19 quarters, 114 dimes, and 30 nickels
You can check answer by plugging values for d, n, and q into
the original equation