Question

A warehouse contains 7250 books in it. Books are being shipped from the warehouse such that the number of books decreased by 150 per day. It will begin to print more books when the warehouse contains less than 2000 books.
Let D be the number of days the warehouse has a shipping box set up inequality involving D that models when the warehouse will print more books. Solve the inequality.

Will the warehouse be printing on the 30th day?

Answer 1

Using an linear function, we have that:

• The inequality is: $-150D + 7250 < 2000$

• The warehouse will start printing more books on the 35th day, hence it won't be printing on the 30th day.

What is a linear function?

A linear function is modeled by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem:

• A warehouse contains 7250 books in it, hence b = 7250.

• Books are being shipped from the warehouse such that the number of books decreased by 150 per day, hence m = -150.

Thus, the number of books each day is modeled by the following function:

$B(D) = -150D + 7250$

It will begin to print more books when the warehouse contains less than 2000 books, hence, the inequality is:

$B(D) < 2000$

$-150D + 7250 < 2000$

Then:

$-150D < -5250$

$150D > 5250$

$D > \frac{5250}{150}$

$D > 35$

The warehouse will start printing more books on the 35th day, hence it won't be printing on the 30th day.

More can be learned about linear functions at brainly.com/question/24808124