Inverse Variation

Question

To balance a seesaw, the distance a person is from the fulcrum is inversely proportional to his or her weight. Roger, who weighs 120 pounds is sitting 6 feet from the fulcrum. Ellen weighs 108 pounds. How far from the fulcrum must she sit to balance the seesaw? Round to the nearest hundredth of a foot.

Answer 1

The relationship is inversely proportional which means that the product of the 2 variables is equal to a constant. As 1 variable increases the other must decrease. In this question the variables are weight and distance from the fulcrum. Therefore:

x = weight

y = distance

So xy = constant

we want Ellen and Roger to be equal to each other so

x1y1 = x2y2

now just solve for y2 and you’ll have your answer!

Answer 2

To balance the seesaw, the product of distance and weight must be the same for both Roger and Ellen. If x is Ellen's distance, then

(120 lbs)(6 ft) = (108 lbs)x

(120)(6) = 108x,

with x in ft. Solve for x and finish from here.