Question 1143524
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            I will show you another way to solve the problem using only one unknown from the very beginning.



<pre>
Let x be the price for a carton of large eggs (the unknown value under the question).


Then Matt bought  {{{112/x}}}  cartoons of large eggs.


The price extra-large eggs is then  (x+1) dollars per cartoons, so he could buy  {{{112/(x+1)}}}  cartoons of extra-large eggs.


The condition says that


    {{{112/x}}} - {{{112/(x+1)}}} = 2.


The setup is completed.

To solve the equation, multiply both sides by x*(x+1).


    112*(x+1) - 112x = 2x*(x+1)

    112x + 112 - 112x = 2x^2 + 2x

    2x^2 + 2x - 112 = 0

    x^2 + x - 56 = 0


Factor left side

    (x-7)*(x+8) = 0


It has two roots, but only positive root  x= 7  makes sense.


<U>ANSWER</U>.  The price of a cartoon of large eggs is $7.


<U>CHECK</U>.   At $7 per cartoon, Matt bough  {{{112/7}}} = 16 cartoons of large eggs.

         At the price (7+1) = 8 dollars per cartoon, Matt could buy  {{{112/8}}} = 14 cartoons of extra-large eggs.

         The difference is 16-14 = 2, in accordance with the condition  (!)
</pre>


You can solve the problem by EITHER of the two ways.


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If you want to see other similar solved problems, look into the lesson

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

in this site.