Math

A drugstore sells a drug costing $85 for $112 and drug costing $175 for $238.
A, If the markup policy of the drugstore is assumed to be linear, write an equation that expresses retail price R in terms of cost C (wholesale price).
B, what does a store pay (to the nearest dollar) for a drug that retails for $185?

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  1. A.) Cost 85, Retail 112
    Cost 175, Retail 238

    For the equation
    (x,R), x = cost
    (85,112), (175,238)

    Since linear, use y = mx + b
    R = mx + b
    slope m = 238 - 112/(175 - 85)
    slope m = 126/90 = 1.4

    R = 1.4x + b
    To find b, plug in (85,112)
    112 = 1.4(85) + b
    112 = 119 + b
    b = -7

    R = 1.4x - 7

    B. R = 1.4x - 7
    185 = 1.4x - 7
    192 = 1.4x
    x = 137

    I am not a tutor, so I am not 100% sure this is how this is done.

    But if you check the orig. given info if seems to work.

    R = 1.4 x - 7
    x = cost, R = retail
    (x,R) = (85,112)
    112 = 1.4(85) - 7
    112 = 119 - 7
    112 = 112

    (x,R) = (175,238)
    238 = 1.4(175) - 7
    238 = 245 - 7
    238 = 238

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  2. a. R = (112/85)C,
    R = 1.32C.

    b. R = 1.32C,
    C = R/1.32 = 185 / 1.32 = 140.

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  3. I favour helper's approach.

    The question states that the markup is linear, but did not say it passes through the origin. That explains why the ratios 112/85 and 238/175 are different.

    According to helper, the markup is 40% less 7$, which works for both given cases.

    So for a retail price of 185, the wholesale price is (185+7)/1.4 = $137.14.

    The only doubt is the negative value -$7, which causes a problem for items where the wholesale price is below 17.5$.

    At wholesale = 17.5, retail equals wholesale! Below that price, items are sold at a loss.

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  4. Since, the problem states to use R and C for the equation, change the x to C.

    So, the equation would be,
    R = 1.4C - 7

    Instead of,
    R = 1.4x - 7

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  5. Yes, I noticed the difference in he ratios; but I assumed the 238 was probably meant to be 231.

    Thanks, MathMate!

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