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13 June, 07:16

5 gallons of diesel weighs 37 pounds. How much does 3 gallons of diesel weigh? Do these quantities (volume and weight) vary directly or inversely? Find the constant of variation.

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  1. 13 June, 07:20
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    22.2 pounds and 1g = 7.4p

    Step-by-step explanation:

    Lets go in an inverse sense, finding firstly the constant variation and then the weight of 3 gallons.

    The constant variation is the relation between gallons of diesel volume and pounds of diesel weight. For thise we would like to find how many pounds of diesel weights 1 gallon. We have the following equality:

    5 gallons = 37 pounds

    Now, lets divide both sided by 5, as we know the equality will still:

    5/5 gallon = 37 / 5 pounds

    1 gallon = 7.4 pounds

    So, this is the constant variations: every extra gallons weights 7.4 pounds. We could also do this in terms of pounds, which means, parting from:

    5 gallons = 37 pounds

    Divide both sides by 37:

    5/37 gallons = 1 pound

    0.081 gallons = 1 pound

    Every extra pound means 0.081 more gallons.

    Now, as we want the weight of 3 gallons we can use our first relation and multiplying by 3:

    1 gallon = 7.4 pounds

    3 gallons = 22.2 pounds
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