Question 1135052

 lauren purchased a box of burgers for 35$ at her usual grocery store. When she got back home she saw a flyer for a different store advertising a price that was 50 cents less per burger. if laura has shopped at the second store she could have bought 8 more burgers for the same price

what was the price of one of the burgers lauren bought?
<pre>Let price of each burger be B
Then we get: {{{matrix(1,3, 35/B, "=", 35/(B - .5) - 8)}}}
{{{matrix(1,3, 35(B - .5), "=", 35B - 8B(B - .5))}}} ------- Multiplying by LCD, B(B - .5)
{{{matrix(1,3, 35B - 17.5, "=", 35B - 8B^2 + 4B)}}}
{{{matrix(1,3, 8B^2 - 4B - 35B + 35B - 17.5, "=", 0)}}}
{{{matrix(1,3, 8B^2 - 4B - 17.5, "=", 0)}}} 
{{{matrix(1,3, 16B^2 - 8B - 35, "=", 0)}}} --------- Multiplying by 2 to CLEAR DECIMAL
{{{matrix(1,3, 16B^2 - 28B + 20B - 35, "=", 0)}}}
4B(4B - 7) + 5(4B - 7) = 0
4B - 7 = 0       OR    4B + 5 = 0
Cost of a burger, or {{{highlight_green(matrix(1,5, B, "=", 7/4, or, "$1.75"))}}}        OR         {{{matrix(1,4, B, "=", - 5/4, "(ignore)")}}}