Question 760541
Let A = number of gold coins
Let b = number os silver coins
Equation 1: {{{A + B = 42}}}
Equation 2: {{{8A + 5B = 246}}}
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Solve equation 1 for one of the variables.
Equation 1: {{{A + B = 42}}}
{{{A = 42 - B}}}
Now plug (42 - B) into equation 2 for A
Equation 2: {{{8A + 5B = 246}}}
{{{8*(42 - B) + 5B = 246}}}
Simplify the equation.
{{{336 - 8B + 5B = 246}}}
Combine like terms.
{{{336 - 3B = 246}}}
Add 3B to both sides
{{{336 = 246 + 3B}}}
Subtract 246 from both sides.
{{{90 = 3B}}}
Divide both sides by 3.
{{{highlight(30 = B)}}}
Now solve for A while using B = 30,
{{{A = 42 - B}}}
{{{A = 42 - (30)}}}
{{{highlight_green(A = 12)}}}