SOLUTION: Joe makes scooters. He sells an average of 500 of them a year and charges $30 for each. He figures for every $1 he raises the price, he will sell 10 fewer scooters. He wants to mak

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Question 763172: Joe makes scooters. He sells an average of 500 of them a year and charges $30 for each. He figures for every $1 he raises the price, he will sell 10 fewer scooters. He wants to make more money. He would like to spend as little time as possible making scooters. If he wants to make $15,900 a year, how much should he charge?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
x is the increase to the number of scooters. 10x is the price increase. The original formula is 500*30=15000. The formula for the increase is:


(500-10x) * (30+x) = 15900


Multiply with FOIL, and simplify to get:


15000+%2B200x+-+10x%5E2+=+15900


Move everything to the right side


0+=+10x%5E2+-+200x+%2B+900


Divide all terms by 10:


0+=+x%5E2+-20x+%2B90


Use the quadratic formula to find x:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ = %2820+%2B-+sqrt%28+400-360%29%29%2F%282%29+ =


=


approximately 13.16 or 6.84.


Charge either $43.16 or $36.84


If it has to be whole dollar increments, then charge $43 or $37. In both cases he would make $15,910.