Question

If John studied 6 hours and scored 69 on his math test, how many hours would he need to study to achieve a score of 92?

Answer 1

To determine how many hours John would need to study to achieve a score of 92, we can establish a relationship between study hours and test scores.

Given the information:

- 6 hours of study = 69 score
- We need to find the hours (let's call it \( x \)) required to achieve a score of 92.

We can assume a linear relationship between study hours and scores.

1. Calculate the score increase:
- \( 92 - 69 = 23 \)

2. Calculate the study hours corresponding to the 69 score:
- For every hour of study, we can find the score increment:
\[
\text{Score increase per hour} = \frac{69}{6} \approx 11.5
\]

3. Determine how many additional hours are needed to achieve the additional score of 23:
- Set up the equation:
\[
11.5 \, \text{(score increase per hour)} \times (\text{additional hours}) = 23
\]
- Rearranging gives:
\[
\text{additional hours} = \frac{23}{11.5} \approx 2
\]

4. Therefore, he would need an additional 2 hours of study. To find the total hours:
\[
\text{Total hours} = 6 + 2 = 8 \text{ hours}
\]

Thus, John would need to study approximately **8 hours** to achieve a score of 92 on his math test.