Question 666459
x = dimes
y = quarters
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Given
.1x + .25y = 3.85
x = y + 7
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Substitute x into the first equation and solve for y, quarters
.1(y+7) + .25y = 3.85
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Distribute .1
.1y + .7 + .25y = 3.85
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Isloate y
.35y = 3.85 - .7
.35y = 3.15
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Divide both sides by .35
{{{highlight_green(y = 9 )}}} quarters
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Substitute y = x-7 into the first equation and solve for x, dimes
.1x + .25(x-7) = 3.85
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Distribute the .25
.1x + .25x - 1.75 = 3.85
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Isolate x
.35x = 3.85 + 1.75
.35x = 5.6
{{{highlight_green(x = 16)}}} dimes
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Check {{{cartoon(
.1(16) + .25(9),
1.60 + 2.25,
3.85)}}}
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