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.

Question

How many points was each multiple choice question worth?

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points

Answer 1

Let \( x \) be the number of points each multiple choice question is worth.

Gretchen's total score can be expressed as: \[ \text{Gretchen's score} = 18x + 19 \]

Ezia's total score can be expressed as: \[ \text{Ezia's score} = 15x + 31 \]

Since their scores are equal, we can set up the equation: \[ 18x + 19 = 15x + 31 \]

To solve for \( x \), first, subtract \( 15x \) from both sides: \[ 18x - 15x + 19 = 31 \] This simplifies to: \[ 3x + 19 = 31 \]

Next, subtract 19 from both sides: \[ 3x = 31 - 19 \] Which simplifies to: \[ 3x = 12 \]

Now, divide both sides by 3 to solve for \( x \): \[ x = \frac{12}{3} = 4 \]

Thus, the value of each multiple choice question is: \[ \boxed{4} \text{ points} \]