document.write( "Question 1153556: Several friends decided to equally share the $525 cost of the set of cookware for a wedding gift. However, before the wedding, 6 more friends joined the others in giving the couple the cookwares. This lowered the contribution of each person by $10. How many friends originally agreed to share of the cost of the cookware? \n" ); document.write( "
Algebra.Com's Answer #775809 by Theo(13342)\"\" \"About 
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x = number of friends who originally agreed to share the cost.
\n" ); document.write( "y = cost per friend.
\n" ); document.write( "total cost = 525.
\n" ); document.write( "x * y = 525
\n" ); document.write( "when 6 friends join, x becomes x + 6
\n" ); document.write( "when the price is dropped by 10 dollars, y becomes y - 10
\n" ); document.write( "total cost is still 525.
\n" ); document.write( "(x + 6) * (y - 10) = 525
\n" ); document.write( "you have two equations that need to be solved simultaneouly.
\n" ); document.write( "they are:
\n" ); document.write( "x * y = 525
\n" ); document.write( "(x + 6) * (y - 10) = 525
\n" ); document.write( "simplify the second equation to get:
\n" ); document.write( "x * y - 10 * x + 6 * y - 60 = 525
\n" ); document.write( "from the first equation, solve for x to get x = 525 / y
\n" ); document.write( "in the second equation, replace x with 525 / y to get:
\n" ); document.write( "525 / y * y - 10 * 525 / y + 6 * y - 60 = 525
\n" ); document.write( "simplify to get:
\n" ); document.write( "525 - 5250 / y + 6 * y - 60 = 525
\n" ); document.write( "multiply both sides of the equation by y to get:
\n" ); document.write( "525 * y - 5250 + 6 * y^2 - 60 * y = 525 * y
\n" ); document.write( "the 525 * y in both sides of the equaton cancels out and you get:
\n" ); document.write( "- 5250 + 6 * y^2 - 60 * y = 0
\n" ); document.write( "reorder the terms in descending order of degree to get:
\n" ); document.write( "6 * y^2 - 60 * y - 5250 = 0
\n" ); document.write( "divide both sides of the equation by 6 to get:
\n" ); document.write( "y^2 - 10 * y - 875 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "y = -25 or y = 35.
\n" ); document.write( "y has to be positive, so y = 35.
\n" ); document.write( "y is the original cost to each friend.
\n" ); document.write( "since x * y = 525, then x = 525 / y = 525 / 35 = 15.
\n" ); document.write( "the original number of friends was 15 and they each would have to pay 35 dollars each.
\n" ); document.write( "6 friends joined for a total of 21 friends.
\n" ); document.write( "525 / 21 = 25.
\n" ); document.write( "the cost of 35 dollars for each friend dropped from 35 dollars per friend to 25 dollars per friend.
\n" ); document.write( "this confirms the solution is correct.\r
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