Question 1150850
1)Shop keeper M sells some goods to N and makes a profit 15% N resells to p at a loss of 5%. If p pays dollar 13.11 how much did M pay for the 
goods
2) a profit 24% was made when a book was sold for dollar 34.10, find the selling price that would have given a profit 28%.
<pre><b><u>1)</b></u>
Let cost to M be C
After M sells the goods to N at a 15% profit, N paid (1 + .15)C = 1.15C
After N sells the goods to P at a 5% loss, P paid (1 - .05)1.15C = .95(1.15C) = 1.0925C 
Since P paid $13.11, then we can say that: 1.0925C = 13.11
Cost to M, or {{{highlight_green(matrix(1,5, C, "=", 13.11/1.0925, "=", "$12"))}}}

<b><u>2)</b></u>
After being sold at a 24% gain, for $34.10, a selling price (P) would yield a 28% profit by using the following PROPORTION: {{{matrix(1,7, (1 + .24)/34.1, "=", (1 + .28)/P, "======>", 1.24/34.1, "=", 1.28/P)}}}
1.24P = 1.28(34.1) ------- Cross-multiplying
Selling price in order to realize a 28% profit, or {{{highlight_green(matrix(1,5, P, "=", 1.28(34.1)/1.24, "=", "$35.20"))}}}