Question

Consider the system of inequalities below.

{34 28-1500
3H + 2S < 1500
10
If y represents the number of hardcover books a bookstore sells in a day and s
represents the number of softcover books it sells in a day, which of the following
statements could be true?
I. The store makes $3 profit on hardcover books and $2 profit on softcover
books. It never makes more than $1500 profit per day.
II. On a very good day, the bookstore sells 1500 books.
III. The bookstore sells at least 10 books per day.
IV. The bookstore never sells more than 10 books per day.
A I only
B II only
C I and III only
DII and IV only

Answer 1

To determine which of the given statements could be true, we analyze each one. Statements I and III are possible.

Step-by-step explanation:

To determine which of the given statements could be true, we need to analyze each one.

I. The store makes $3 profit on hardcover books and $2 profit on softcover books. It never makes more than $1500 profit per day.

To check if this statement could be true, we need to find the maximum values for y and s such that the profit remains below $1500. We have the inequalities:

• 3y + 2s < 1500
  (Profit on hardcover books + Profit on softcover books < $1500)
• 34y + 28s < 1500
  (Total number of hardcover books + Total number of softcover books < 1500)

II. On a very good day, the bookstore sells 1500 books.

This statement could be true if the total number of hardcover books and softcover books sold is exactly 1500.

III. The bookstore sells at least 10 books per day.

This statement could be true as there are no specific constraints on the minimum number of books sold.

IV. The bookstore never sells more than 10 books per day.

This statement is not possible as there are no constraints on the maximum number of books sold.

From the analysis, we can see that statements I and III could be true. Therefore, the correct answer is C) I and III only.