Question 280059
Set-Up
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Let A = 2 Cent stamps
Let B = 3 Cent stamps
Let C = 5 Cent stamps
Notice that each statement is in terms of the 2 cent stamps.
Equation 1: {{{A + 50 = B}}}
Equation 2: {{{A - 25 = C}}}
Equation 3: {{{0.02A + 0.03B + 0.05C = 16.25}}}

Solution
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Use substitution.
Substitute equation 1 and 2 into equation 3
Equation 3: {{{0.02A + 0.03B + 0.05C = 16.25}}}
{{{0.02A + 0.03*(A + 50) + 0.05*(A - 25) = 16.25}}} Simplify
{{{0.02A + 0.03A + 1.5 + 0.05A - 1.25 = 16.25}}} Combine like terms
{{{0.1A + 0.25 = 16.25}}} subtract 0.25 from both sides
{{{0.1A = 16}}} Divide both sides by 0.1
{{{highlight(A = 160)}}}

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Now plug 160 into equations 1 & 2 for A
Equation 1: {{{A + 50 = B}}}
{{{160 + 50 = B}}}
{{{highlight(210 = B)}}}

Equation 2: {{{A - 25 = C}}}
{{{160 - 25 = C}}}
{{{highlight(135 = C)}}}

Check the answers:
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You can check your answers by plugging in the values into equation 3
Equation 3: {{{0.02A + 0.03B + 0.05C = 16.25}}}
{{{0.02*(160) + 0.03*(210) + 0.05*(135) = 16.25}}}
{{{3.2 + 6.3 + 6.75 = 16.25}}}
{{{highlight(16.25 = 16.25)}}}