Question

The amount a spring stretches varies directly as the weight of the object attached to it. If an 8-ounce weight stretches a spring 10 centimeters, how much weight will stretch it to 15 centimeters?

A) 12 ounces
B) 20 ounces
C) 24 ounces
D) 30 ounces

Answer 1

Using the direct variation relationship and setting up a ratio, it was determined that a weight of 12 ounces will stretch the spring to 15 centimeters, which is option A.

Step-by-step explanation:

The phenomenon being described is an example of direct variation, where one quantity depends directly on another. In this case, the amount a spring stretches is directly proportional to the weight attached to it.

Given that 8 ounces stretches the spring 10 centimeters, we can set up a ratio to find out how much weight will stretch it to 15 centimeters. If 8 ounces corresponds to 10 cm, then 'x' ounces (the weight we are trying to find) will correspond to 15 cm. The ratio is therefore:

8 ounces / 10 cm = x ounces / 15 cm

By cross-multiplying, we get:

8 ounces × 15 cm = 10 cm × x ounces

120 = 10x

Now, we solve for 'x' by dividing both sides by 10:

x = 120 / 10

x = 12 ounces

Therefore, it will take 12 ounces to stretch the spring to 15 centimeters, which corresponds to option A.