Question 1135052
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<pre>
At the first store the price for one burger was  {{{35/n}}} dollars, where "n" was the number of burgers in the box.


At the second store there were (n+8) burgers in their box for the same cost of 35 dollars per box,

so the cost of one single burger was  {{{35/(n+8)}}}  dollars.   


The difference in price for one single burger is 50 cents = 0.5 dollar, which gives you an equation


    {{{35/n}}} - {{{35/(n+8)}}} = 0.5   dollars.    (1)


To solve this equation, multiply both sides by 2*n*(n+8). You will get


    70(n+8) - 70n = n*(n+8).


Simplify and then solve this quadratic equation


    70n + 70*8 - 70n = n^2 + 8n

    n^2 + 8n - 560 = 0.


Factor left side


    (n+28)*(n-20) = 0.


Only positive root  n = 20  is meaningful - so it is the solution.


<U>Answer</U>.  There were 20 burgers in the box at the first store at the price  {{{35/20}}} = $1.75 per one burger.


<U>CHECK</U>.  I will check if the equation (1) is satisfied.

        The price for 1 burger at the first store is  {{{35/20}}} = {{{3500/20}}} cents = 175 cents.

        The price for 1 burger at the second store is  {{{35/28}}} dollars = {{{3500/28}}} = 125 cents, or exactly 0.5 dollars less.

        So the problem is solved correctly (!)
</pre>

Solved.


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I like this approach: &nbsp;it is short and straightforward, &nbsp;and at every step of building the base equation (1) you follow 
exactly to the problem's description. &nbsp;It prevents you of making errors - as much as possible.


In this site, &nbsp;there are several lessons, &nbsp;where you can find similar problems explained ans solved

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/Challenging-word-problems-solved-using-quadratic-equations.lesson>Challenging word problems solved using quadratic equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Had-they-sold.lesson>Had they sold . . .</A>


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<U>Be careful</U>:  &nbsp;&nbsp;The post &nbsp;(the solution) &nbsp;by &nbsp;@swincher4391 &nbsp;has an error !