Math
posted by Tha .
Bosley's Pet Foods buys dog kibbl for $19.50 per bag, less 40%. The store's overhead is 33 1/3% of the selling price, and the desired profit is 10% of the selling price.
(a) At what price per bag should the dog food be sold?
(b) At this price, what is the rate of markup on cost?
(c) What is the breakeven price?

Arithmetic is used to solve the problem although algebra can also be used.
Cost price = $19.50 19.50*0.40 = $11.70
The selling price includes
 33 1/3 % of overhead
 10 % of profit
So the fraction of cost in selling price
= 100%  33 1/3  10 = 56 2/3%
Therefore selling price
= cost / fraction of cost
= $11.70 / (56 2/3%)
= $11.70 / (170/300)
= $11.70 * 300/170
= $20.65
Check:
Profit (10%) = 20.65*0.1 = $2.07
Overhead (33 1/3%) = 20.65*(1/3)= 6.88
Cost price = 20.652.076.88=11.70
So the answer is correct. 
(b) the markup on cost is the profit divided by the cost price. It should be different from 33 1/3%.
(c) the break even price is the selling price less the profit, i.e. zero profit.