Question

The distance a spring will stretch varies directly with how much weight is attached to the spring. If a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? Round to the nearest tenth of an inch.


10 in.

9.1 in.

8.1 in.

8.9 in.

Answer 1

The distance a spring stretches varies directly with the weight attached to it. This means we can set up a ratio based on the information given.

Let \( d \) be the distance the spring stretches, and \( w \) be the weight attached to the spring. From the problem, we have:

\[
\frac{d_1}{w_1} = \frac{d_2}{w_2}
\]

Where:
- \( d_1 = 9 \) inches (the stretch with 100 pounds)
- \( w_1 = 100 \) pounds
- \( w_2 = 90 \) pounds
- \( d_2 \) is the stretch we want to find with 90 pounds.

Now, substituting the known values into the equation:

\[
\frac{9}{100} = \frac{d_2}{90}
\]

To solve for \( d_2 \), cross-multiply:

\[
9 \cdot 90 = 100 \cdot d_2
\]

\[
810 = 100d_2
\]

Now, divide both sides by 100 to find \( d_2 \):

\[
d_2 = \frac{810}{100} = 8.1
\]

So, the spring will stretch **8.1 inches** with 90 pounds attached. Therefore, the correct answer is:

**8.1 in.**