grade 11 math help?

Question

when compact disks are sold for $13 each. a music store can sell 300 in a month. for every $1 increase in the price, the number sold drops by 30. if the total sales revenue is $3360. how many compact disks were sold?

answers
a)240
b)210
c)180
d)300
e)150

please if you could explain how to do it not just give me the answer that would be great

Answer 1

The answer is b) 210. This question is easier to figure out by trial and error, 210 is 3 drops less than 300, so the price is $16, and $16 times 210 is $3,360.

Price x quantity = $3,360
($13 + X) x (300-- 30X) = 3,360
-30X^2 --90x + 3900 = 3360
X^2+3x -- 130 = --112
X^2 + 3x -- 18 = 0
(x+6 ) (x-3) =0

for this to = 0
x = --6 or + 3

--6 is outside the bounds but x = 3 works

P = 13 + 3 = 16
q = 300 --90 = 210

Answer 2

It can't be 300 because if you multiply it by 13 you get 3900 dollars that's 540 more dollars than actually made.You can guess and check with the rest of the answers. If you look at A 240, that means they had to raise the price by two dollars so it would be 3600 dollars, that's still too much so go to another one. Let's check B 210, that means they had to raise the price by three dollars because the number of disks sold dropped by 90. If you multiply, you get 3360, which is the amount of revenue for the month. This isn't the real way of finding the answer but it works because you have something to go from the answers.

Answer 3

The answer would be b) 210
At $13 total would be 300 x 13 = $3900
By deducting 30 disks the total would be 300 - 30 = 270 x $14. =$3780.
You would have to deduct 30 from the total of 270 @15 and then amount would then be thus 15 x 240 =$3,600. Then $16 x 210 =$3,360.
Therefore by deducting 30 from 300, then from 270 then from 240 then 210 and by adding $1 each time you will get the total of $3,360 at $16.
Hope this helped.