#### Explanation:

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 $\left(90 + 5 x\right)$

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

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

$50 {x}^{2} - 100 x = 400 \mathmr{and} {x}^{2} - 2 x - 8 = 0$ or

$\left(x - 4\right) \left(x + 2\right) = 0 \therefore x = 4 , x = - 2$

when $x = 4$ , the price of jackets be 200-10*4= $160 and number of sells of jacket is $90 + 5 \cdot 4 = 110$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 $90 + 5 \cdot \left(- 2\right) = 80$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]