The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10lb watermelon on a hanging scale, the spring stretched 5in. Write an equation that relates the length L that the spring stretches to the weight w. How many pounds does a watermelon weigh if it stretch the spring 6in?

Question

Mathematics

Cristina Russell

6 July, 09:09

The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10lb watermelon on a hanging scale, the spring stretched 5in. Write an equation that relates the length L that the spring stretches to the weight w. How many pounds does a watermelon weigh if it stretch the spring 6in?

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Answers (1)

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Lin · Answer 1

Answer: A watermelon weighs 12 lb if it stretches the spring 6in.

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that length, L varies directly with weight, W, if we introduce a constant of proportionality, k, the expression becomes

L = kW

When W = 10 and L = 5, then

5 = 10k

k = 5/10 = 0.5

Therefore, the equation that relates the length L that the spring stretches to the weight W is

L = 0.5W

Therefore, if L = 6 inch, then

6 = 0.5W

W = 6/0.5 = 12 lb