Question 1196789

a grocer bought some oranges at a cost of 8 for 96 cents and then 2/3 times as many at a cost of 6 for 1.02. In order to make a profit 50%, he must sell all of them at a price of a dozen for $m. Find the value of m in dollars.
<pre>Let N be the number of oranges purchased 1<sup><b>st</sup></b>
Then amount paid for the 1<sup><b>st</sup></b> purchase = {{{matrix(1,3, (.96/8)N, "=", .12N)}}}
With {{{matrix(1,5, 2/3, of, "N,", or, 2N/3)}}} being the amount purchased after, the amount paid for the 2<sup><b>nd</sup></b> purchase = {{{matrix(1,5, (1.02/6)(2N/3), "=", .17(2N/3), "=", .34N/3)}}}

With sale price of $m per dozen, each orange was sold for {{{m/12}}}

    Total number of oranges purchased: {{{matrix(1,5, N + 2N/3, "=", (3N + 2N)/3, "=", 5N/3)}}}

Total cost of {{{5N/3}}} oranges: {{{matrix(1,5, .12N + .34N/3, "=", (.36N + .34N)/3, "=", .7N/3)}}}

To realize a 50% profit, we then get: {{{matrix(1,3, (m/12)(5N/3), "=", 1.5 * (.7N/3))}}}
                                            {{{highlight_green(matrix(3,3,       5mN/36, "=", .5(.7N), 5mN, "=", 36(.35N), m, "=", 36(.35N)/(5N)))}}}
                                             {{{highlight_green(matrix(1,5, highlight(m), "=", 36(.07), "=", highlight("$2.52")))}}}</pre>