document.write( "Question 1203188: A bakery baked 1200 cupcakes and packed them into boxes. There were 5/8 as many big boxes as small boxes. Each big box contained 7 more cupcakes than each small box. There were 240 more cupcakes packed in big boxes than in the small boxes. How many cupcakes were there in each small box? \n" ); document.write( "

Algebra.Com's Answer #838552 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A bakery baked 1200 cupcakes and packed them into boxes.
\n" ); document.write( "There were 5/8 as many big boxes as small boxes.
\n" ); document.write( "Each big box contained 7 more cupcakes than each small box.
\n" ); document.write( "There were 240 more cupcakes packed in big boxes than in the small boxes.
\n" ); document.write( "How many cupcakes were there in each small box?
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem is to solve in two steps.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "        First step\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Total x cupcakes packed in big   boxes\r\n" );
document.write( "total y cupcakes packed in small boxes\r\n" );
document.write( "\r\n" );
document.write( "From the problem\r\n" );
document.write( "\r\n" );
document.write( "    x + y = 1200    (1)\r\n" );
document.write( "    x - y =  240    (2)\r\n" );
document.write( "\r\n" );
document.write( "Add equations (1) and (2).  You will get\r\n" );
document.write( "\r\n" );
document.write( "    2x = 1440  -->  x = 1440/2 = 720              (the number of cupcakes packed in big boxes)\r\n" );
document.write( "\r\n" );
document.write( "Then from eq(1)  y = 1200 - x = 1200 - 720 = 480  (the number of cupcakes packed in small boxes).\r\n" );
document.write( "     \r\n" );
document.write( "\r\n" );
document.write( "        Second step\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let z be the number of cupcakes in each small box (= the value under the problem's question)\r\n" );
document.write( "Then the number of cupcases in each big box is (z+7).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of small boxes is         (3)\r\n" );
document.write( "\r\n" );
document.write( "The number of big   boxes is    (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "According to 5the problem, the ratio of the number of big boxes (4)\r\n" );
document.write( "to the number of small boxes (3) is 5/8\r\n" );
document.write( "\r\n" );
document.write( "    = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and find z\r\n" );
document.write( "\r\n" );
document.write( "     = \r\n" );
document.write( "\r\n" );
document.write( "    3z*8 = 5*2*(z+7)\r\n" );
document.write( "\r\n" );
document.write( "    24z  = 10z + 70\r\n" );
document.write( "\r\n" );
document.write( "    24z - 10z = 70\r\n" );
document.write( "\r\n" );
document.write( "        14z   = 70\r\n" );
document.write( "\r\n" );
document.write( "          z   = 70/14 = 5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The number of cupcakes in each small box is 5 (five).\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );