document.write( "Question 436995: How would one go about writing 48/n(n-2)+22 as a quadratic equation?
\n" ); document.write( "I'm working on the problem:
\n" ); document.write( "A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaining mugs for $3 above the original cost per mug, she made a total profit of $22.
\n" ); document.write( "Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.
\n" ); document.write( "Just by looking at the question I know that the mugs she bought were $4 each and she got 12 of them then sold 10 of them. But I'm lost trying to write out the quadratic equation.
\n" ); document.write( "I know it should look like \"ax%5E2%2Bbx%2Bc=0\"
\n" ); document.write( "Thank for any help on this! \n" ); document.write( "
Algebra.Com's Answer #302324 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaining mugs for $3 above the original cost per mug, she made a total profit of $22.
\n" ); document.write( "Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.
\n" ); document.write( ":
\n" ); document.write( "Price paid for each mug = \"48%2Fn\"
\n" ); document.write( ":
\n" ); document.write( "No. of mugs sold = (n-2)
\n" ); document.write( ":
\n" ); document.write( "Selling price = \"48%2Fn\" + 3
\n" ); document.write( ";
\n" ); document.write( "Revenue should = cost + profit
\n" ); document.write( ":
\n" ); document.write( "Total revenue = 48 + 22 = $70:
\n" ); document.write( ":
\n" ); document.write( "#sold * Price sold = total revenue
\n" ); document.write( "(n-2) * [\"48%2Fn\" + 3] = 70
\n" ); document.write( "FOIL
\n" ); document.write( "48 + 3n - 96/n - 6 = 70
\n" ); document.write( "combine like terms
\n" ); document.write( "3n - 96/n + 48 - 6 - 70 = 0
\n" ); document.write( "3n - 96/n - 28 = 0
\n" ); document.write( "Multiply equation by n, forming a quadratic equation:
\n" ); document.write( "3n^2 - 28n - 96 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(3n +8)(n-12) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "n = 12 mugs originally bought
\n" ); document.write( ":
\n" ); document.write( "Check
\n" ); document.write( "Cost: 48/12 = $4
\n" ); document.write( "Sold: 10 * 7 = $70 (cost + profit)
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