document.write( "Question 1143524: Matt brought several cartons of large eggs for $112. If he had bought extra-large eggs costing $1 more per carton, he would have 2 less cartons of eggs for the same money. How much did he pay for a carton of large eggs? \n" ); document.write( "

Algebra.Com's Answer #764350 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "There are many ways to solve the problem using algebra. Here is an outline of one of them (not necessarily the best).

\n" ); document.write( "Let the number of cartons be x and the price of each carton be y. Then

\n" ); document.write( " $\"xy+=+112\"$
\n" ); document.write( " $\"%28x-2%29%28y%2B1%29+=+112\"$

\n" ); document.write( "Since both expressions are equal to 112, set them equal to each other and simplify:

\n" ); document.write( " $\"xy+=+%28x-2%29%28y%2B1%29\"$
\n" ); document.write( " $\"xy+=+xy%2Bx-2y-2\"$
\n" ); document.write( " $\"x+=+2y%2B2\"$

\n" ); document.write( "Substitute that expression for x in the first equation:

\n" ); document.write( " $\"%282y%2B2%29y+=+112\"$

\n" ); document.write( "Solve for y and then use that value to determine the value of x.

\n" ); document.write( "By far the easiest way to solve the problem is simply to play with numbers:

\n" ); document.write( "112 = 16*7
\n" ); document.write( "112 = 14*8

\n" ); document.write( "Those pairs of numbers satisfy the conditions of the problem:
\n" ); document.write( "16 cartons of eggs for $7 each;
\n" ); document.write( "14 cartons of eggs for $8 each \n" ); document.write( "

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