Question 316301

First step, name your variables.
Let M be the number of correct multiple choice problems and T be the number of correct true/false problems.
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"28 questions were answered correctly"
With our variables,
1.{{{M+T=28}}}
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"mutilple choice questions are worth 3 points, true false are worth 2 points....score of 77 points"
2.{{{3M+2T=77}}}
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You now have 2 equations with 2 unknowns, M and T.
Multiply eq. 1 by (-3) and add to eq. 2,
{{{-3M-3T+3M+2T=-84+77}}}
{{{-T=-7}}}
{{{highlight( T=7)}}}
Then from eq. 1,
{{{M+7=28}}}
{{{highlight( M=21)}}}
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Twenty one multiple questions and seven T/F questions were answered correctly.