Question 278824
Set-Up
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Let A = Number of Nickels
Let b = Number of Dimes
Equation 1: {{{A*0.05 + B*0.1 = 5.65}}}
Equation 2: {{{(A + 8)*0.05 + 2*B*0.1 = 10.45}}}

Solution:
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You can divide every term in equation 1 by .05
Equation 1: {{{A*0.05 + B*0.1 = 5.65}}}
{{{A + 2B = 113}}} Subtract 2B from both sides
{{{A = 113 - 2B}}}

Now we can plug (113 - 2B) into equation 2 for A
Equation 2: {{{(A + 8)*0.05 + 2*B*0.1 = 10.45}}}
{{{((113 - 2B) + 8)*0.05 + 2*B*0.1 = 10.45}}} Simplify
{{{(121 - 2B)*0.05 + B*0.2 = 10.45}}} Simplify
{{{6.05 - 0.1*B + 0.2*B = 10.45}}} Simplify
{{{6.05 + 0.1B = 10.45}}} Subtract 6.05 from both sides
{{{0.1B = 4.40}}} Divide both sides by 0.1
{{{highlight(B = 44)}}}

Now plug 44 into the modified equation 1 for B
{{{A = 113 - 2B}}}
{{{A = 113 - 2*(44)}}}
{{{A = 113 - 88}}}
{{{highlight(A = 25)}}}