Question 676951
Establish variables
n = nickels
d = dimes
q = quarters
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Given equations
n+d+q = 75
.05n + .1d + .25q = 7.25
n = 5d
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Substitute the third equation into the first equation
5d + d + q = 75
6d + q = 75
q = 75 - 6d
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Substitute into the second equation
.05(5d) + .1d + .25(75-6d) = 7.25
.25d + .1d + 18.75 - 1.5d = 7.25
-1.15d = 7.25 - 18.75
-1.15d = -11.5
{{{highlight_green(d = 10)}}} dimes
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n = 5(10) = {{{highlight_green(n=50)}}}nickels
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q = 75 - 6(10) = 75 - 60 {{{highlight_green(q=15)}}} quarters
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