Question

Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s^2+9s-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?

s < 42
s > 42
s > 51
s < 51

Answer 1

s^2 + 9s - 142 > 2000
s^2 + 9s - 142 - 2000 > 0
s^2 + 9s - 2142 > 0
(s-42)(s+51) > 0

s - 42 > 0
s > 42

s + 51 > 0
s > -51.......will not work

answer is : s > 42

Answer 2

Answer:
`s>42`

Explanation:

Given: The profit, p, made by the company is modeled by the function

`s^2+9s-142`.

According to the question, we have

`s^2 + 9s - 142 > 2000\\\Rightarrow s^2 + 9s - 142 - 2000 > 0\\\Rightarrow s^2 + 9s - 2142 > 0\\\Rightarrow (s-42)(s+51) > 0\\\Rightarrow s>42\ \ ,\ s>-51`

But
`s>-51` is not possible.

Hence,
`s>42` is the answer.