document.write( "Question 1200905: Hi
\n" ); document.write( "Shop p had 200 apples and 300 oranges. Shop q had 240 apples and 100 oranges. How many apples and oranges must be moved from q to p so that half of the fruits in p and 3/4 of the fruits in q are apples in the end.
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Algebra.Com's Answer #835141 by Theo(13342)\"\" \"About 
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p had 200 apples and 300 oranges.
\n" ); document.write( "q had 240 apples and 100 oranges.
\n" ); document.write( "total number of fruits in p is 500.
\n" ); document.write( "total number of fruitis in q is 340.
\n" ); document.write( "let x = the number of apples to be moved from q to p.
\n" ); document.write( "let y = the number of oranges to be moved from q to p.
\n" ); document.write( "when all is said and done, you want half of the fruits in p and 3/4 of the fruits in q to be apples.
\n" ); document.write( "you have 2 equations that need to be solved simultaneously.
\n" ); document.write( "they are:
\n" ); document.write( "200 + x = .5 * (500 + x + y)
\n" ); document.write( "240 - x = .75 * (340 - x - y)
\n" ); document.write( "simplify to get:
\n" ); document.write( "200 + x = 250 + .5 * (x + y)
\n" ); document.write( "240 - x = 255 - .75 * (x + y)
\n" ); document.write( "subtract 200 from both sides of the first equation and subtract .5 * (x + y) from both sides of the first equation to get:
\n" ); document.write( "x - .5 * (x + y) = 50
\n" ); document.write( "subtract 240 from both sides of the second equation and add .75 * (x + y) to both sides of the second equation to get:
\n" ); document.write( ".75 * (x + y) - x = 15
\n" ); document.write( "the two equations that need to be solved simultaneously are:
\n" ); document.write( "x - .5 * (x + y) = 50
\n" ); document.write( ".75 * (x + y) - x = 15
\n" ); document.write( "simplify and combine like terms in both equaations to get:
\n" ); document.write( ".5x - .5y = 50
\n" ); document.write( "-.25x + .75y = 15
\n" ); document.write( "multiply both sides of the second equation by 2 and leave the first equqtion as is to get:
\n" ); document.write( ". 5x - .5y = 50
\n" ); document.write( "-.5 x + 1.5y = 30
\n" ); document.write( "add the two equations together to get:
\n" ); document.write( "y = 80
\n" ); document.write( "replace y with 80 in the first equqtion to get:
\n" ); document.write( ".5x - .5*80 = 50
\n" ); document.write( "simplify to get:
\n" ); document.write( ".5x - 40 = 50
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 180
\n" ); document.write( "your solution should be x = 180 and y = 80
\n" ); document.write( "shop p started with 200 apples and 300 oranges.
\n" ); document.write( "add 180 apples and 80 oranges to get 380 apples and 380 oranges.
\n" ); document.write( "the number of apples is 50% of the total for shop p.
\n" ); document.write( "shop q started with 240 apples and 100 oranges
\n" ); document.write( "subtract 180 apples and 80 oranges to get 60 apples and 20 oranges.
\n" ); document.write( "the number of apples is 75% of the total for shop q.
\n" ); document.write( "your solution appears to be:
\n" ); document.write( "180 apples and 80 oranges are moved from q to p.\r
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