Question 1135052
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There are many ways to solve this kind of problem.  The following is likely not the easiest -- just what seems to me the "obvious" way to get started.<br>
Let n be the number of burgers and p be the price of each.  Then<br>
{{{np = 35}}} the cost of the burgers she bought was $35
{{{(n+8)(p-1/2) = 35}}} the cost of 8 more burgers at a price 50 cents less each would also have been $35<br>
{{{np = (n+8)(p-1/2)}}}
{{{np = np-(1/2)n+8p-4}}}
{{{8p = (1/2)n+4}}}
{{{16p = n+8}}}
{{{n = 16p-8}}}<br>
Substitute that back into the first equation:<br>
{{{p(16p-8) = 35}}}
{{{16p^2-8p = 35}}}
{{{16p^2-8p-35 = 0}}}
{{{(4p-7)(4p+5) = 0}}}
{{{p = 7/4 = 1.75}}} or {{{p = -5/4 = -1.25}}}<br>
A negative price doesn't make any sense, so the price per burger she paid was $1.75.<br>
CHECK: $35 at $1.75 each --> 20 burgers;
28 burgers at $1.25 each = $35