Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.
How many points was each multiple choice question worth?
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Okay so, first off, we have to know how many points they obtained and with that, knowing that they both got the same score on the test.
So, we will call the points of the multiple choice as "p" and we know they got added by 18 and 31 respectively.
We can represent the score Gretchen obtained by the equation: \(18p+19\)
We can represent the score Ezia obtained by the equation: \(15p+31\)
So, we know they got the same score on this test, so that means \(18p+19\) and \(15p+31\) yield the same result, so therefore:
And now it's just a matter of solving that little equation.