Question

Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+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 > 42 is the answer

Answer 2

Answer:

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

→→ p=s²+9 s-142, where s is the number of T-shirts sold.

We want profit on T shirt sold should be more than $ 2,000.So,the profit equation can be written as,

⇒s²+9 s-142>2000

$s^{2}+9 s-142-2000>0\\\\ s^{2}+9 s-2142>0\\\\s^{2}+51 s- 42 s-2142>0\\\\ s(s+51)-42(s+51)>0\\\\(s-42)(s+51)>0\\\\ s-42>0\\\\s>42$

→We will neglect, s+51> or <0,because number of T-shirts sold can't be negative.

Or,→→there is second way, mark points, 42 and -51 on the number line, and substitute , number greater than 42 on the profit Inequality,which is s²+9 s-2142>0, which gives ,s>42.

Option B: s >42