5. The force, in pounds, required to loosen a bolt with a wrench varies inversely with the length of the wrench, in inches. If the constant of variation is 1500 . what is the length of the wrench if 250 pounds of force are needed to loosen a bolt?

This is a problem of inverse variation. In an inverse variation, the product of the two variables is always constant. In this case, the force (F) required to loosen a bolt varies inversely with the length (L) of the wrench. The constant of variation (k) is given as 1500. The formula for inverse variation is F = k/L. We are asked to find the length of the wrench (L) when the force (F) is 250 pounds. We can rearrange the formula to solve for L: L = k/F. Substituting the given values, we get L = 1500/250.