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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?



Answer :

sydneyhenderson
The multiply choice were worth 4 points. 
Gretchen= 18x+19
Ezia= 15x+31

So basically you can enter any number. At first I picked 3 and then I did the math and I got 73 points for Gretchen and 76 points for Ezia. 

Then I pick four and then I got 91 points for them both. This is how I got the answer: 

18x+19=15x+31
18(4)+19=15(4)+31
72+19=60+31
91=91

I hope this get a clear understanding of how I got the answer :D

The correct answer is:

4 points per multiple choice question

Explanation:

Let x be the amount each multiple choice question is worth. Since Gretchen answered 18 of them correctly, we would write this as 18x. Adding the 19 points for the essay question, we have 18x+19.

Since Ezia answered 15 multiple choice questions correctly, we would write this as 15x. Adding the 31 points for the essay question, we have 15x+31.

Since they had the same score, we set these equal to one another:

18x+19 = 15x+31

To solve this, first subtract 15x from each side:

18x+19-15x = 15x+31-15x

3x+19 = 31

Subtract 19 from each side:

3x+19-19 = 31-19

3x=12

Divide each side by 3:

3x/3 = 12/3

x = 4

Each question is worth 4 points.

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