A sporting goods store sells 90 jackets for $200 dollars each. Each $10 decrease in price would result in 5 more jackets sold. How do you find the number of jackets sold and the selling price to give revenues of $17600 from jacket sales?

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Answer 1 · 2018-08-03T11:38:00

To earn #$176000# cost price and number of sale should be#($160 and 110) or ($220 and 80)#

Let the number of decrease of #$10# in cost be #x#

Then, new reduced cost price is #$(200- 10 x)# and

increased sale of jackets is #(90+5 x) #

Revenues earned is #(200-10 x) (90+5 x)= 17600# or

# -50 x^2 +100 x +18000=17600# or

# 50x^2 -100 x =400 or x^2 -2 x -8=0# or

#(x-4)(x+2)=0 :. x= 4 , x=-2#

when #x=4# , the price of jackets be #200-10*4= $160#

and number of sells of jacket is # 90+5*4=110# and revenue

earned is #110*160=$17600#.

when #x=-2# , the price of jackets be #200-10*(-2)= $220#

and number of sells of jacket is # 90+5*(-2)=80# and revenue

earned is #80*220=$17600#.

To earn #$176000# cost price and number of sale should be

#$160 and 110 or $220 and 80# [Ans]