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A box of apples costs $2,a box of pears costs $3,and a box of plums costs $4.
\n" ); document.write( "If 8 fruit boxes cost $23 together, what is the largest possible number of them that contain plums?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of boxes of apples
\n" ); document.write( "Let y = no. of boxes of pears
\n" ); document.write( "Let z = no. of boxes of plums
\n" ); document.write( ":
\n" ); document.write( "no. of boxes equation
\n" ); document.write( "x + y + z = 8
\n" ); document.write( ":
\n" ); document.write( "total cost equation
\n" ); document.write( "2x + 3y + 4z = 23
\n" ); document.write( ":
\n" ); document.write( "Looks like 3 boxes of plums would be the max, see if that will work
\n" ); document.write( "Cost for 3 boxes = $12
\n" ); document.write( ":
\n" ); document.write( "Adjust the equations to reflect 3 boxes of plums
\n" ); document.write( "x + y = 8 - 3
\n" ); document.write( "x + y = 5
\n" ); document.write( "y = (5-x)
\n" ); document.write( "and
\n" ); document.write( "2x + 3y = 23 - 12
\n" ); document.write( "2x + 3y = 11
\n" ); document.write( "Replace y with (5-x)
\n" ); document.write( "2x + 3(5-x) = 11
\n" ); document.write( "2x + 15 - 3x = 11
\n" ); document.write( "2x - 3x = 11 - 15
\n" ); document.write( "-x = -4
\n" ); document.write( "x = 4 boxes of apples
\n" ); document.write( "then
\n" ); document.write( "5 - 4 = 1 boxes of pears
\n" ); document.write( ":
\n" ); document.write( "We can't have less than 1 box of pears, so it has to be 3 boxes of plums
\n" ); document.write( ":
\n" ); document.write( "Check solutions
\n" ); document.write( "4 + 1 = 3 = 8
\n" ); document.write( "and
\n" ); document.write( "2(4) + 3(1) + 4(3) = 23 \n" ); document.write( "