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March 28, 2017

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The Juice Problem. A store sells a 1-liter container of
juice for 75¢ and a 2-liter container for $1.40. Assume
that the cost varies linearly with the number of liters, and find the slope of the line that shows the relationship.
How many liters would be in a container that cost
$3.35?

  • Math - ,

    First find the rule for the cost.
    C(1) = 0.75
    C(2) = 1.40 (difference = 0.65)
    C(3) = 2.05
    C(4) = ...
    C(x) = mx+0.10
    Find m, and then solve for
    C(x) = 3.35

  • Math - ,

    I am still confused, I understand finding the difference and that being 0.65. What I am not sure about is where you wrote c(x)=mx+0.10. I know that the C stands for cost, should the x be a y? I know that m stands for slope but what is the 0.10? I really do not understand linear equations.

  • Math - ,

    To express the equation in a more familiar form, it could be
    y=mx+b
    where b is the y-intercept, meaning the value of y when x=0. In this context, it represents a fixed cost, for example, the cost of the container.

    We can find b by taking the difference of C(1)-m, or 0.75-0.65 = 0.10.
    We therefore end up with
    y=0.65x + 0.10

    So the question reduces to when y=3.35, solve for x in
    3.35=0.65x + 0.10

  • Math - ,

    Okay that clears it up. Thank you very much for your help.

  • Math - ,

    You're welcome!

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