TEAS 7 Math Practice Test | Every Answer Explained - Free Printable

The problem presented in the image is related to finding the number of questions a second friend answered correctly based on the percentage of correct answers from a first friend. Let's break it down step by step.

Problem Statement:

- One friend got 96 questions correct out of 120 questions.
- The second friend took an exam with 75 questions.
- We need to determine how many questions the second friend answered correctly, assuming they had the same percentage of correct answers as the first friend.

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Step-by-Step Solution:

#### Step 1: Calculate the percentage of correct answers for the first friend.
The percentage of correct answers is given by the formula:
\[
\text{Percentage} = \left( \frac{\text{Number of Correct Answers}}{\text{Total Number of Questions}} \right) \times 100
\]
For the first friend:
\[
\text{Percentage} = \left( \frac{96}{120} \right) \times 100
\]

Simplify the fraction:
\[
\frac{96}{120} = \frac{4}{5}
\]

Now calculate the percentage:
\[
\text{Percentage} = \left( \frac{4}{5} \right) \times 100 = 80\%
\]

So, the first friend answered 80% of the questions correctly.

#### Step 2: Apply the same percentage to the second friend's exam.
The second friend took an exam with 75 questions. If they also answered 80% of the questions correctly, the number of correct answers can be calculated as:
\[
\text{Number of Correct Answers} = \left( \frac{80}{100} \right) \times 75
\]

Simplify the calculation:
\[
\text{Number of Correct Answers} = 0.8 \times 75 = 60
\]

#### Step 3: Verify the solution using proportions.
We can also solve this using proportions. If the first friend's ratio of correct answers to total questions is the same as the second friend's ratio, we can set up the proportion:
\[
\frac{96}{120} = \frac{x}{75}
\]

Cross-multiply to solve for \( x \):
\[
96 \times 75 = 120 \times x
\]
\[
7200 = 120x
\]

Divide both sides by 120:
\[
x = \frac{7200}{120} = 60
\]

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Final Answer:

The second friend answered \(\boxed{60}\) questions correctly.