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31 March, 14:36

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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  1. 31 March, 16:14
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    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
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