Find the number of correct and incorrect answers

The player of a trivia game receives 100 points for each correct answer and loses 25 points for each incorrect answer. Leona answered a total of 30 questions and scored a total of 2125.  Find the number of correct and incorrect answers that she had.

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Use a system of equations.

x = number of correct answers
y = number of incorrect answers

x + y = 30  {there were 30 total questions}
100x - 25y = 2125  {100 points for correct answer and -25 points for incorrect answer}

-100x - 100y = -3000  {multiplied top equation by -100}
100x - 25y = 2125  {bottom equation stays the same}
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-125y = -875  {added the two equations}
y = 7  {divided each side by -125}

x + y = 30  {first original equation}
x + 7 = 30  {substituted 7, in for y, into first original equation}
x = 23  {subtracted 7 from each side}

23 correct answers
7 incorrect answers

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