The amount of force, F, needed to lift an object using a lever varies inversely as the length, l, of the lever. When a 24-inch lever is used, a force of 240 pounds is needed. How much force is needed if a 36-inch long lever is used?

I already know A. 120 pounds is wrong

A. 120 pounds XXX

B. 160 pounds

C. 252 pounds

D. 360 pounds

The variation is an inverse variation.; so, 160 pounds of force is needed for a 36-inch long lever

Given that F varies inversely as L, the variation is represented as:

Express as an equation

-- where k represents the constant of variation

Make k the subject

When F = 240, L = 24.

So, we have:

Substitute 5760 for k in

When L = 36, we have:

Divide both sides by 36

Rewrite as:

Hence, 160 pounds of force is needed for a 36-inch long lever

Read more about variation at:

link

F = 160 pounds

B. 160 pounds

Step-by-step explanation:

F = k / l

Where,

F = amount of force needed

l = length of the lever

k = constant of proportionality

F = 240 when l = 24 inch

F = k / l

240 = k / 24

Cross product

240*24 = k

k = 5,760

Find F when l = 36 inch

Recall, k = 5,760

F = k / l

= 5,760 / 36

= 160

F = 160 pounds

The correct answer is B. 160 pounds