SOLUTION: A club treasurer has $28.45 consisting of nickels, dimes, and quarters. She has 9 more nickels than dimes and three times as many dimes as quarters. How many does she have of each

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Question 175616: A club treasurer has $28.45 consisting of nickels, dimes, and quarters. She has 9 more nickels than dimes and three times as many dimes as quarters. How many does she have of each coin?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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treasurer has $28.45 consisting of nickels, dimes, and quarters.
She has 9 more nickels than dimes and three times as many dimes as quarters.
How many does she have of each coin?
:
Write an equation for each statement:
:
"treasurer has $28.45 consisting of nickels, dimes, and quarters."
.05n + .10d + .25q = 28.45
:
"She has 9 more nickels than dimes"
n = d + 9
:
" and three times as many dimes as quarters."
d = 3q
or we can write it:
q = 1%2F3d
:
How many does she have of each coin?
:
Using the 1st equation substitute:
(d+9) for n
1%2F3d for q
.05(d+9) + .10d + .25(1%2F3d) = 28.45
.05d + .45 + .10d + .25%2F3d = 28.45
.15d + .25%2F3d = 28.45 - .45
.15d + .25%2F3d = 28.00
Multiply equation by 3 to get rid of the denominator
.45d + .25d = 84
.70d = 84
d = 84%2F.7
d = 120 dimes
:
Find nickels:
n = 120 + 9
n = 129 nickels
:
Find quarters:
q = 1%2F3*120
q = 40 quarters
;
:
Check solutions in the 1st equation:
.05(129) + .10(120) + .25(40) =
6.45 + 12.00 + 10.00 = 28.45; confirms our solutions