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Question Find the number of points xx a student needs to score on a 50-point test to get a 78% score. The proportion is x50=78100\frac{x}{50} = \frac{78}{100}.

Studdy Solution

STEP 1

Assumptions
1. The test is worth 50 points.
2. The desired test score is 78%.
3. We are looking for the number of points xx a student needs to score to achieve a 78% score.
4. The proportion will be set up with xx points out of 50 points equal to 78 out of 100, since percentages are out of 100.

STEP 2

First, we need to express the desired test score as a proportion. The test score of 78% means the student needs to score 78 points out of 100 possible points.
Student’s pointsTotal points possible=78100\frac{\text{Student's points}}{\text{Total points possible}} = \frac{78}{100}

STEP 3

Now, we need to set up the proportion using the total points possible on the test, which is 50 points. We will use xx to represent the number of points the student needs to score.
x50=78100\frac{x}{50} = \frac{78}{100}

STEP 4

To solve for xx, we will cross-multiply the terms in the proportion.
x×100=78×50x \times 100 = 78 \times 50

STEP 5

Perform the multiplication on both sides of the equation.
100x=3900100x = 3900

STEP 6

Now, we will divide both sides of the equation by 100 to solve for xx.
100x100=3900100\frac{100x}{100} = \frac{3900}{100}

STEP 7

Calculate the value of xx.
x=39x = 39
The student needs to score 39 points on the test to get a test score of 78%.

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