SOLUTION: Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. The number of quarters is 5 less than three-fourths the number of dimes. The number of silver

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Question 341951: Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars. The number of quarters is 5 less than three-fourths the number of dimes. The number of silver dollars is 7 more than five-eighths the number of dimes. How many coins of each kind are in her collection?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars.
d + q + $ = 116
:
The number of quarters is 5 less than three-fourths the number of dimes.
q = 3%2F4d - 5
:
The number of silver dollars is 7 more than five-eighths the number of dimes.
$ = 5%2F8d + 7
:
How many coins of each kind are in her collection?
Using the 1st equation replace q & $
d + 3%2F4d - 5 + 5%2F8d + 7 = 116
Common denominator
d + 6%2F8d + 5%2F8d + 2 = 116
d + 11%2F8d = 116 - 2
d + 11%2F8d = 114
Multiply by 8 to get rid of the denominator, results:
8d + 11d = 912
d = 912%2F19
d = 48 dimes
then
q = 3%2F4(48) - 5
q = 36 - 5
q = 31 quarters
and
$ = 5%2F8(48) + 7
$ = 37 silver dollars
:
Check total: 48 + 31 + 37 = 116