document.write( "Question 1198564: I told a fruit seller to give me Rs. 1680 worth of passion fruits. After he gave me the passion fruits, I forced him to give me 4 extra passion fruits for free. He complained that because of giving me the extra passion fruits, he is getting Rs. 120 per dozen less on this transaction than the original price. How many passion fruits did get (including the 4 extra passion fruits)? \n" ); document.write( "

Algebra.Com's Answer #832196 by Theo(13342) $\"\"$ $\"About$

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x is the number of passion fruit.
\n" ); document.write( "p is the price for each passion fruit.\r
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\n" ); document.write( "\n" ); document.write( "your first eqution is x * p = 1680.\r
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\n" ); document.write( "\n" ); document.write( "when he gets 4 more passion fruits for free, the price per dozen pawsion fruit becomes less by 120 per dozen.
\n" ); document.write( "120 / 12 = less by 10 per passion fruit.\r
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\n" ); document.write( "\n" ); document.write( "your second equation is (x + 4) * (p - 10) = 1680\r
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\n" ); document.write( "\n" ); document.write( "simplify that eqution to get xp - 10x + 4p - 40 = 1680
\n" ); document.write( "subtract 1680 from both sides of the equation to get xp - 10x + 4p - 1720 = 0\r
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\n" ); document.write( "\n" ); document.write( "from the first equation, solve for p to get p = 1680/x
\n" ); document.write( "replace p in the second equation with 1680/x to get:
\n" ); document.write( "x * 1680/x - 10x + 4 * 1680/x - 1720 = 0
\n" ); document.write( "simplify to get:
\n" ); document.write( "1680 - 10x + 6720/x - 1720 = 0
\n" ); document.write( "multiply both sides of that equation by x to get:
\n" ); document.write( "1680x - 10x^2 + 6720 - 1720x = 0
\n" ); document.write( "combine like terms and reorder the equation in descending order of degree to get:
\n" ); document.write( "-10x^2 - 40x + 6720 = 0
\n" ); document.write( "multiply both sides of this equation by -1 to get:
\n" ); document.write( "10x^2 + 40x - 6720 = 0
\n" ); document.write( "divide both sides of this equation by 10 to get:
\n" ); document.write( "x^2 + 4x - 672 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "x = -28 or x = 24
\n" ); document.write( "since x can't be negative, then x = 24 looks like it's your solution.
\n" ); document.write( "in the first equation, replace x with 24 to get 24p = 1680
\n" ); document.write( "solve for p to get p = 70.
\n" ); document.write( "in your second equation, replace x with 24 to get 28 * p = 1680
\n" ); document.write( "solve for p to get p = 60.\r
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\n" ); document.write( "\n" ); document.write( "the requirements of the problem are satisfied.
\n" ); document.write( "when he receives 24 passion fruits, the price is 70 for each passion fruit.
\n" ); document.write( "when he receives 4 extra passion fruits for free, he gets 28 passion fruits for the same cost of 1680.
\n" ); document.write( "the price per passion fruit becomes 60.\r
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\n" ); document.write( "\n" ); document.write( "your solution is that he got 28 passion fruits, including the 4 that he got for free.\r
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