The distance a spring stretches varies directly with the force applied to it. If a 7-pound weight stretches a spring a distance of 24.5 inches, how far will the spring stretch if a 12-pound weight is applied?

d/12 = 24.5/7

do i cross multipe

that's one way.

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To find out how far the spring will stretch if a 12-pound weight is applied, we need to apply the concept of direct variation. Direct variation means that when two variables are directly proportional, one variable increases or decreases in direct proportion to the other variable.

In this case, the force applied to the spring (in pounds) is directly proportional to the distance the spring stretches (in inches). This can be represented by the equation:

force = constant * distance

Since we know that a 7-pound weight stretches the spring a distance of 24.5 inches, we can use these values to find the constant of variation. Let's call the constant "k". Using the equation above, we can write:

7 = k * 24.5

Now we can solve for k:

k = 7 / 24.5
k ≈ 0.2857

Now that we have the constant (k), we can calculate how far the spring will stretch when a 12-pound weight is applied. Let's call this distance "x". Using the equation of direct variation:

12 = 0.2857 * x

To find x, we need to isolate it by dividing both sides of the equation by 0.2857:

x = 12 / 0.2857
x ≈ 42

Therefore, the spring will stretch approximately 42 inches when a 12-pound weight is applied.