Question

If John studied 6 hours and got a 69 on his math test, how many hours would he need to study to get a 92?

Answer 1

To find out how many hours John would need to study to improve his score from 69 to 92, we can use a proportional relationship based on the hours studied and the scores achieved.

Let's denote:
- \( H_1 = 6 \) hours (studied for the first test)
- \( S_1 = 69 \) (score from the first test)
- \( H_2 \) = hours required for a score of \( S_2 = 92 \)

If we assume that the relationship between hours studied and score is linear, we can set up a proportion:

\[
\frac{S_1 - 0}{H_1} = \frac{S_2 - 0}{H_2}
\]

We need to find \( H_2 \).

First, we can define that a score of 0 corresponds to 0 hours (if we assume a score of zero without studying). Thus:

1. From the first test:

\[
\frac{69 - 0}{6} = \frac{69}{6} \approx 11.5 \quad \text{(score per hour)}
\]

2. From the second test:

\[
\frac{92 - 0}{H_2} = \frac{92}{H_2}
\]

Now, we can set the two equations equal to find \( H_2 \):

\[
\frac{69}{6} = \frac{92}{H_2}
\]

Cross-multiplying gives:

\[
69 \cdot H_2 = 92 \cdot 6
\]

Now, calculate \( 92 \cdot 6 = 552 \):

\[
69H_2 = 552
\]

Now, divide both sides by 69:

\[
H_2 = \frac{552}{69} \approx 8
\]

So, John would need to study approximately **8 hours** to achieve a score of 92.