Question

At Lucille's Boutique, the monthly number of sales M is approximately related to the number of employee hours (P) worked by M=48+6P−3−−−−−√. How many hours must the employees work to have 300 monthly sales?

Answer 1

1767 hours

Explanation:

Given equation:
`M= 48+6√(P-3)`

Where M is monthly number of sales and P is the number of employee hours.

Now, finding number of hours employee worksto have 300 monthly sales.

Using given equation to find the number of employee hours (P).

`M= 48+6√(P-3)`

Subtituting the value of M, which is 300.

⇒
`300= 48+6√(P-3)`

Subtracting both side by 48

⇒
`300-48=6√(P-3)`

⇒
`252= 6√(P-3)`

Dividing both side by 6

⇒
`(252)/(6) = √(P-3)`

⇒
`42= √(P-3)`

Taking square of the number on both side.

remember, √a²= a

⇒
`42^(2) = P-3`

⇒
`1764= P-3`

Adding 3 on both side

⇒
`P= 1764+3`

∴ P= 1767

Hence, 1767 hours must the employees work to have 300 monthly sales.