document.write( "Question 849855: There are 3 times as many pears as oranges. A group of children receive 5 oranges abd 8 pears each. All the oranges are given away, but there are 21 pears left. How many children are there, and how many oranges are there? \n" ); document.write( "
Algebra.Com's Answer #511771 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
There are 3 times as many pears as oranges. A group of children receive 5 oranges and 8 pears each. All the oranges are given away, but there are 21 pears left. How many children are there, and how many oranges are there?\r
\n" ); document.write( "\n" ); document.write( "Im sorry ..let me rephrase ..how do i write the equation? Like, let x be number of children and y the number of oranges ..how do you do the equation if its like that ? 'Cause in my homework it saya it should be like that ..
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Let x be number of children and y the number of oranges. \r\n" );
document.write( "\r\n" );
document.write( "All the oranges are given away and each child has 5 oranges.\r\n" );
document.write( "\r\n" );
document.write( "So the number of oranges is 5 times the number of children.  So\r\n" );
document.write( "one equation is\r\n" );
document.write( "\r\n" );
document.write( "                          y = 5x\r\n" );
document.write( "\r\n" );
document.write( "Since there are 3 times as many pears as oranges,\r\n" );
document.write( "\r\n" );
document.write( "the number of pears is 3 times the number of oranges, so\r\n" );
document.write( "\r\n" );
document.write( "the number of pears = 3y\r\n" );
document.write( "\r\n" );
document.write( "Since there were 21 pears left, \r\n" );
document.write( "\r\n" );
document.write( "there were only 3y-21 pears received, because we subtract the 21\r\n" );
document.write( "from the number of pears to get the number of pears given out.\r\n" );
document.write( "\r\n" );
document.write( "Since each child received 8 pears,\r\n" );
document.write( "\r\n" );
document.write( "The number of pears received = 8 times the number of children.\r\n" );
document.write( "\r\n" );
document.write( "                      3y-21 = 8x\r\n" );
document.write( "                          \r\n" );
document.write( "So we have this system of equations:\r\n" );
document.write( "\r\n" );
document.write( "                          y = 5x\r\n" );
document.write( "                      3y-21 = 8x\r\n" );
document.write( "\r\n" );
document.write( "We use the method of substitution.  We substitute 5x\r\n" );
document.write( "for y in the second equation.\r\n" );
document.write( "\r\n" );
document.write( "                   3(5x)-21 = 8x\r\n" );
document.write( "                     15x-21 = 8x   \r\n" );
document.write( "\r\n" );
document.write( "Add +21 to both sides \r\n" );
document.write( "\r\n" );
document.write( "                     15x-21 = 8x                   \r\n" );
document.write( "                        +21     +21\r\n" );
document.write( "                    -----------------\r\n" );
document.write( "                     15x    = 8x+21\r\n" );
document.write( "\r\n" );
document.write( "Add -8x to both sides of the equation:\r\n" );
document.write( "\r\n" );
document.write( "                      15x    = 8x+21\r\n" );
document.write( "                      -8x     -8x\r\n" );
document.write( "                    -----------------\r\n" );
document.write( "                       7x    =    21\r\n" );
document.write( "                     \r\n" );
document.write( "Divide both sides by 7\r\n" );
document.write( "\r\n" );
document.write( "                        x    =    3\r\n" );
document.write( "\r\n" );
document.write( "Substitute x=3 into        y = 5x      \r\n" );
document.write( "                           y = 5(3) = 15\r\n" );
document.write( "\r\n" );
document.write( "So there were x=3 children and y=15 oranges \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's all you were asked for but we must find the number of\r\n" );
document.write( "pairs so we can check the problem.\r\n" );
document.write( "\r\n" );
document.write( "Since the number of pears = 3y, 3(15) = 45\r\n" );
document.write( "\r\n" );
document.write( "So there were 45 pears. \r\n" );
document.write( "\r\n" );
document.write( "Now we check the sentences in the problem, with\r\n" );
document.write( "

\n" ); document.write( "3 children, 15 oranges, and 45 pears.
\n" ); document.write( "
\r\n" );
document.write( "There are 3 times as many pears as oranges. \r\n" );
document.write( "\r\n" );
document.write( "That checks because 3×15 = 45\r\n" );
document.write( "

\n" ); document.write( "A group of children receive 5 oranges...All the oranges are given away,
\n" ); document.write( "
\r\n" );
document.write( "The oranges check because 5×3 = 15 \r\n" );
document.write( "

\n" ); document.write( "...and 8 pears each...but there are 21 pears left.
\n" ); document.write( "
\r\n" );
document.write( "8×3 = 24 pears given out plus the 21 left over is 24+21=45\r\n" );
document.write( "So that checks.\r\n" );
document.write( "\r\n" );
document.write( "So 3 children, 15 oranges, and 45 pears is correct.     \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );