Math  /  Algebra

QuestionSo far this semester, Nora is averaging a score of 75.4 points on math tests, which is 7.5%7.5 \% higher than her average last semester. What was the average of her scores last semester?
Round your answer to the nearest tenth.

Studdy Solution

STEP 1

What is this asking? If Nora's current math test average is 7.5% higher than last semester's average, what was her average last semester? Watch out! Don't add or subtract the percentage directly to the current average!
We need to figure out what the original 100% was.

STEP 2

1. Set up the relationship between this semester's average and last semester's average.
2. Solve for last semester's average.

STEP 3

Let xx be Nora's average score last semester.
This is what we're trying to find!

STEP 4

The 7.5% increase can be written as the decimal 0.075.
Remember, "percent" means "per hundred," so we divide the percentage by 100 to get the decimal form.

STEP 5

This semester's average is 7.5% *more than* last semester's average.
This means we take last semester's average (xx), and add 7.5% *of* last semester's average (0.075x0.075 \cdot x) to it.
This gives us this semester's average of 75.4.
So, our equation is: x+0.075x=75.4 x + 0.075 \cdot x = 75.4

STEP 6

We've got xx plus 0.075x0.075x.
Remember that xx is really just 1x1x, so we can rewrite our equation as: 1x+0.075x=75.4 1x + 0.075x = 75.4 Combining the xx terms gives us: 1.075x=75.4 1.075x = 75.4 This tells us that 75.4 is equal to 107.5% of last semester's average.

STEP 7

To find xx, we need to divide both sides of the equation by **1.075**.
Why? Because that will give us 1x1x on the left side, which is just xx, exactly what we want! 1.075x1.075=75.41.075 \frac{1.075x}{1.075} = \frac{75.4}{1.075} x=75.41.075 x = \frac{75.4}{1.075}

STEP 8

Now, we just divide 75.4 by 1.075: x70.13953488 x \approx 70.13953488

STEP 9

The problem asks us to round to the nearest tenth.
Looking at the hundredths place, we see a 3, which is less than 5.
So, we round down, and our final answer is **70.1**.

STEP 10

Nora's average score last semester was approximately **70.1** points.

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