Question 698340
Let A = # of Quarters
Let B = # of Dimes
Equation 1: {{{A + B = 68)
Equation 2: {{{0.25A + 0.1B = 15.05}}}
Solve equation 1 for one of the variables
Equation 1: {{{A + B = 68)
{{{A = 68 - B}}}
Plug (68 - B) into equation 2 for A
Equation 2: {{{0.25A + 0.1B = 15.05}}}
{{{0.25*(68 - B) + 0.1B = 15.05}}}
Simplify
{{{17 - 0.25B + 0.1B = 15.05}}}
Combine like terms
{{{17 - 0.15B = 15.05}}}
Subtract 17 from both sides
{{{-0.15B = -1.95}}}
Divide both sides by -0.15
{{{highlight(B = 13)}}}
Now plug 13 into equation 1 for B
Equation 1: {{{A + B = 68)
{{{A + (13) = 68}}}
Subtract 13 from both sides
{{{highlight_green(A = 55)}}}
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There are 13 dimes