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Elementary problem

  1. Oct 9, 2015 #1
    1. The problem statement, all variables and given/known data
    A supermarket always makes 40% gross margin on its cereals. So if it sells a box for $1, it has paid the supplier 60 c. When items are sold at a special offer price, the suppliers are expected to reduce their prices so that the supermarket still makes the same percentage gross margin.

    A particular cereal normally sells for $1.50 a box. This week there is a special offer which gives the customer 3 boxes for the price of 2.

    By how much has the supplier of this cereal had to reduce the price of each special offer box?

    Answer is $0.30

    2. Relevant equations



    3. The attempt at a solution

    Before the offer: $1.5 x 6/10 = $0.90
    After the offer: $2/3 x 6/10 = $0.40
    Reduction in price = $0.90 - $0.40= $0.50
     
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  3. Oct 9, 2015 #2

    Ray Vickson

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    You say "...if it sells a box for $1, it has paid 60 c..." That is incorrect: paying 60 c and selling for $1 is a markup of 66.67%, not the 40% you claim.
     
  4. Oct 9, 2015 #3

    SteamKing

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    But cost margin ≠ % markup

    If p = selling price and mc = marginal cost, then price-cost margin is figured on the basis of the selling price, not the marginal cost.

    ∴ margin = (p - mc) / p

    In this case:

    p = $1.00
    mc = $0.60

    margin = (1.00 - 0.60) / 1.00 = 0.40 = 40%

    http://www.amosweb.com/cgi-bin/awb_nav.pl?s=gls&c=dsp&k=price-cost+margin
     
  5. Oct 9, 2015 #4

    SteamKing

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    I think the store is offering 3 boxes of cereal at the old price for 2 boxes, so if you buy 3 boxes of cereal during the promotional period, you would pay 2 × $1.50 / box = $3.00.
    Remember, you are still getting 3 boxes of cereal out of the deal, not 2 boxes.
     
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