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

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

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

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

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

$- 50 x^{2} + 100 x + 18000 = 17600$ $-50 x^2 +100 x +18000=17600$ or

$50 x^{2} - 100 x = 400 or x^{2} - 2 x - 8 = 0$ $50x^2 -100 x =400 or x^2 -2 x -8=0$ 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]