Question

The distance a spring will stretch varies directly how much weight is attached to the spring if a spring stretches 6 inches with 80 pounds attached how far will it stretch with 55 pounds attached? Round to the nearest 10th of an inch

Answer 1

The spring will stretch 4.1 inches

Explanation:

Direct Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

y = kx

Where k is the constant of proportionality.

Let's call:

y = distance a spring stretches

x = weight attached to the spring

We know when x=80 pounds, y=6 inches, thus:

6 = 80k

Solve for k:

`k=(6)/(80)=(3)/(40)`

The equation is now:

`\displaystyle y = (3)/(40)x`

When x=55 pounds are attached:

`\displaystyle y = (3)/(40)\cdot 55`

Calculating:

y = 4.1 inches

The spring will stretch 4.1 inches