Question 692850
Set up:
A = # of correct answers
B = # of wrong answers
Equation 1: {{{18 = 9A - 5B}}}
Equation 2: {{{30 = A + B}}}
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Solve equation 2 for one of the variables. I soled for A
{{{A = 30 - B}}}
Now plug (30 - B) into equation 1 for A
Equation 1: {{{18 = 9A - 5B}}}
{{{18 = 9*(30 - B) - 5B}}}
Simplify
{{{18 = 270 - 9B - 5B}}}
Combine like terms
{{{18 = 270 - 14B}}}
Subtract 270 from both sides
{{{-252 = -14B}}}
Divide both sides by -14
{{{highlight(18 = B)}}}
Now plug 18 into equation 2 for B
Equation 2: {{{30 = A + B}}}
{{{30 = A + (18)}}}
Subtract 18 from both sides
{{{highlight_green(12 = A)}}}