**Lever Word Problems**

- Mae Dupp weighted 120 pounds and sat on one end of a teeter-totter 8 feet from the center. Fess Dupp weighted 160 pounds and sat on the other side. How far (in feet) from the fulcrum (balance point) must Fess sit to balance point is at the center of the board?

Solution

Read the problem and determine the unknown. The question asks how far from the fulcrum Fess sits, so

Let x = Fess’s distance from fulcrum in feet.

Mae weighs 120 pounds and sits on one end of the teeter-totter.

Mae sits 8 feet from the center.

Fess weighed 160 pounds and sat on the other side. We have already found that we would let x equal Fess’s distance.

w_{1}d_{1 = }w_{2}d_{2 where w is weight and d is distance.}

w_{1 = 120} d_{1 = 8} w_{2 = 160} d_{2 = x}

120(8) = 160x

960 = 160x

x = 6

So Fess must sit 6 feet from the fulcrum.

- Bill Ding was digging up his yard to plant a garden. He hit a large rock and got a crowbar to raise the rock to the surface. The crowbar was 6 feet long and the rock was later found to weigh 80 pounds Bill used another rock as the fulcrum and exerted a force equal to 16 pounds on the end of the crowbar in order to raise the rock to a point of balance. How far was the fulcrum from the 80-pound rock?

Solution

Read the problem and determine the unknown. The question asks how far from the fulcrum Fess sits, so

Let x = distance in feet of 80-pound rock from fulcrum.

**Equation**

w_{1}d_{1 = }w_{2}d_{2 where w is weight and d is distance.}

w_{1 = 16} d_{1 = 6 – x} w_{2 = 80} d_{2 = x}

16(6 – x) = 80x

96 – 16x = 80x

-96x = -96

x = 1

So the fulcrum was 1 foot from the rock.

- A weight of 60 pounds rests on the end of an 8-foot lever and is 3 feet from the fulcrum. What weight must be placed on the other end of the lever to balance the 60-pound weight?

Let x = unknown weight in pounds

**Diagram**

5x = 60(3) = 180

x = 36

**Answer**

A 36 pound weight will balance the 60 pound weight

- Four girls decided to use the same teeter-totter. Two of them weighing 75 pounds and 50 pounds, respectively, sat on opposite ends of the 12-foot board which had the balance point at the center. The third girl weighting 60 pounds got on the same side as the one weighing 50 pounds and sat 5 feet from the fulcrum. Where must the fourth girl sit so the teeter-totter is balanced if she weighs 40 pounds?

Let x = unknown weight in pounds

**Diagram**

5x = 60(3) = 180

x = 36

**Answer**

A 36 pound weight will balance the 60 pound weight

- A 200-pound weight rests on one end of a lever, 12 feet from the fulcrum. What weight, resting on the opposite end and 3 feet from the fulcrum, would make a balance?

- The boys take a 12-foot-long board and rest it on a large rock to make a teeter-totter. If the boys sit on opposite ends of the board and weigh 50 pounds and 70 pounds, respectively, how far from the fulcrum will the 70-pound boy be if they balance?

- A window in Patty O’ Cover house is stuck. She takes an 8-inch screwdriver to pry open the window. If the screwdriver rests on the sill (fulcrum) 3 inches from the window and Patty O’ Cover has to exert a force of 10 pounds on the other end to pry open the window, how much force was the window exerting?

- A 35-pound weight is 2 feet from the fulcrum, and a 75-pound weight on the same side is 10 feet from the fulcrum. If a weight on the other end 6 feet from the fulcrum balances the first two, how much does it weigh?

- A lever 10 feet long has a 100-pound weight on one end and a 150-pound weight on the other. If the fulcrum is in the center, in what location must an 80-pound weight be placed so that the lever will balance?

- Batman and Robin go out to play. Batman, who weighs 90 pounds, sits on one end of a 14-foot teeter-totter. Its balance point is at the center of the board. Robin, who weighs 120 pounds, climbs on the other end and slides toward the center until they balance. What is Robin’s distance from her end of the teeter-totter when they balance?