Question 597014
Hi, there-- 
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Let x be the number of problems Terry got right.
Let y be the number of problems Terry got wrong.
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Since a right answer adds 4 points, the number of points for right answers is 4x.
Since a wrong answer subtracts 1 point, the number of points for wrong answers is -y.
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The total number of problems (right and wrong) is 25, so
{{{x+y=25}}}
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The total score (points for right answers minus points for wrong) is 85, so
{{{4x+(-y)=85}}}
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Solve the system of equations using substitution. Rewrite the first equation in terms of y.
{{{x+y=25}}}
{{{y=25-x}}}
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Substitute 25-x for y in the second equation.
{{{4x+(-y)=85}}}
{{{4x+(-(25-x))=85}}}
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Simplify.
{{{4x-25+x=85}}}
{{{5x-25=85}}}
{{{5x=85+25}}}
{{{5x=110}}}
{{{x=22}}}
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Terry has 22 right answers.
Terry has 25-22=3 wrong answers.
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CHECK
Does this combination give a score of 85? 22*4=88 and 3*(-1)=-3. 88-3=85...YES!
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That's it. Feel free to email via gmail if you have questions about this solution.
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Ms.Figgy
math.in.the.vortex@gmail.com