# Elementary problem

1. Oct 9, 2015

### icystrike

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

2. Oct 9, 2015

### Ray Vickson

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.

3. Oct 9, 2015

### SteamKing

Staff Emeritus
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

4. Oct 9, 2015

### SteamKing

Staff Emeritus
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.