Question

the pressure applied to a leverage bar varies inversely as the distance from the object. if 150 pounds is required for a distance of 10 inches from the object, how much pressure is needed for a distance of 3 inches?
500 pounds
45 pounds
5 pounds
450 pounds

Explanation:

Step1: Define inverse variation formula

Let \( P \) be pressure and \( d \) be distance. Inverse variation: \( P = \frac{k}{d} \), where \( k \) is constant.

Step2: Find constant \( k \)

Given \( P = 150 \) when \( d = 10 \). Substitute into formula: \( 150 = \frac{k}{10} \). Solve for \( k \): \( k = 150 \times 10 = 1500 \).

Step3: Calculate pressure for \( d = 3 \)

Use \( k = 1500 \) and \( d = 3 \) in \( P = \frac{k}{d} \): \( P = \frac{1500}{3} = 500 \)? Wait, no, wait. Wait, inverse variation: as distance decreases, pressure increases. Wait, wait, maybe I made a mistake. Wait, no, let's check again. Wait, inverse variation: \( P_1d_1 = P_2d_2 \). So \( 150 \times 10 = P_2 \times 3 \). Then \( P_2 = \frac{150 \times 10}{3} = \frac{1500}{3} = 500 \)? But wait, the options have 500? Wait, the options are 500, 45, 5, 450. Wait, maybe I messed up. Wait, no, inverse variation: pressure varies inversely with distance, so \( P = \frac{k}{d} \). So when distance is 10, pressure 150: \( k = 150*10 = 1500 \). Then when distance is 3, \( P = 1500/3 = 500 \). So the answer is 500 pounds? But wait, the options have 500. Wait, but let me check again. Wait, the problem says "pressure applied to a leverage bar varies inversely as the distance from the object". So inverse variation: \( P \propto \frac{1}{d} \), so \( P_1d_1 = P_2d_2 \). So \( 150 * 10 = P_2 * 3 \). So \( P_2 = (15010)/3 = 500 \). So the answer is 500 pounds? But wait, the options include 500. So that's correct? Wait, but maybe I misread the distance. The problem says "10 inches" (wait, the original problem has "10 inches" or "10 inches"? Wait, the user's problem: "10 inches from the object, how much pressure is needed for a distance of 3 inches?" So yes, 15010=1500, 1500/3=500. So the answer is 500 pounds. Wait, but the options have 500 as the first option. So that's correct.

Answer:

500 pounds