SOLUTION: terry did all 25 problems on his test and got an 85. scores are computed by giving 4 points for each right answer and subtracting one for each wrong answer. how many problems did t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: terry did all 25 problems on his test and got an 85. scores are computed by giving 4 points for each right answer and subtracting one for each wrong answer. how many problems did t      Log On


   

Question 597014: terry did all 25 problems on his test and got an 85. scores are computed by giving 4 points for each right answer and subtracting one for each wrong answer. how many problems did terry get right and wrong?
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
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%2By=25
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The total score (points for right answers minus points for wrong) is 85, so
4x%2B%28-y%29=85
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Solve the system of equations using substitution. Rewrite the first equation in terms of y.
x%2By=25
y=25-x
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Substitute 25-x for y in the second equation.
4x%2B%28-y%29=85
4x%2B%28-%2825-x%29%29=85
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Simplify.
4x-25%2Bx=85
5x-25=85
5x=85%2B25
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