17. A bookstore is placing an order for new books and magazines. Each book costs $15, and each magazine costs $5. The store can spend at most $1,000 on these books and magazines. Additionally, each book takes up 2 square feet of space, and each magazine takes up 1 square foot of space. The store has only 50 square feet of display space available for the new items. The following system of inequalities can be used to determine possible combinations of books, x, and magazines, y, the store can order: 15x+5y≤1000

Question

2x+y≤50

Which combinations of books, x, and magazines, y, can the bookstore order?
A) 20 books and 15 magazines
B) 10 books and 30 magazines
C) 50 books and 0 magazines
D) 40 books and 5 magazines

18. The carnival is arriving in the neighborhood! Leo has saved up $15 to spend at the carnival on food and attractions. Food items cost $4 each and attractions cost $2 each. Leo uses the expression 4a + 2b to determine the total cost for a food items and b attractions.

Select one of the following combinations of food items and attractions that Leo can afford with his $15 budget:
A) 2 food items and 4 attractions
B) 3 food items and 2 attractions
C) 1 food item and 5 attractions
D) 0 food items and 8 attractions

19. Liam and his friends are hosting a bake sale to raise funds for their school trip. They decided to sell cookies for $3 each and muffins for $5 each. Their goal is to raise at least $300, but they want to sell no more than 80 items in total.

Select one of the following combinations that Liam can sell to make at least $300 while keeping the total items sold to a maximum of 80:
A) 50 cookies and 30 muffins
B) 30 cookies and 25 muffins
C) 25 cookies and 30 muffins
D) 40 cookies and 20 muffins

Answer 1

Let's analyze each question one at a time.

17.

We have the inequalities:

1. \(15x + 5y \leq 1000\)
2. \(2x + y \leq 50\)

We will check each option to see which satisfies both inequalities.

A) 20 books and 15 magazines:

• \(15(20) + 5(15) = 300 + 75 = 375 \leq 1000\) (True)
• \(2(20) + 15 = 40 + 15 = 55 \leq 50\) (False)

B) 10 books and 30 magazines:

• \(15(10) + 5(30) = 150 + 150 = 300 \leq 1000\) (True)
• \(2(10) + 30 = 20 + 30 = 50 \leq 50\) (True)

C) 50 books and 0 magazines:

• \(15(50) + 5(0) = 750 + 0 = 750 \leq 1000\) (True)
• \(2(50) + 0 = 100 + 0 = 100 \leq 50\) (False)

D) 40 books and 5 magazines:

• \(15(40) + 5(5) = 600 + 25 = 625 \leq 1000\) (True)
• \(2(40) + 5 = 80 + 5 = 85 \leq 50\) (False)

The only combination that satisfies both conditions is B) 10 books and 30 magazines.

---

18.

We know that Leo can spend at most $15, and the cost expression for his spending is \(4a + 2b\).

We will check each option to see if \(4a + 2b \leq 15\):

A) 2 food items and 4 attractions:

• \(4(2) + 2(4) = 8 + 8 = 16 \leq 15\) (False)

B) 3 food items and 2 attractions:

• \(4(3) + 2(2) = 12 + 4 = 16 \leq 15\) (False)

C) 1 food item and 5 attractions:

• \(4(1) + 2(5) = 4 + 10 = 14 \leq 15\) (True)

D) 0 food items and 8 attractions:

• \(4(0) + 2(8) = 0 + 16 = 16 \leq 15\) (False)

The only combination that Leo can afford is C) 1 food item and 5 attractions.

---

19.

Liam is selling cookies for $3 each and muffins for $5 each, and he wants to raise at least $300 while selling no more than 80 items.

Let \(c\) be the number of cookies and \(m\) be the number of muffins.

The inequalities we are examining are:

1. \(3c + 5m \geq 300\)
2. \(c + m \leq 80\)

Let's check each option:

A) 50 cookies and 30 muffins:

• \(3(50) + 5(30) = 150 + 150 = 300 \geq 300\) (True)
• \(50 + 30 = 80 \leq 80\) (True)

B) 30 cookies and 25 muffins:

• \(3(30) + 5(25) = 90 + 125 = 215 \geq 300\) (False)

C) 25 cookies and 30 muffins:

• \(3(25) + 5(30) = 75 + 150 = 225 \geq 300\) (False)

D) 40 cookies and 20 muffins:

• \(3(40) + 5(20) = 120 + 100 = 220 \geq 300\) (False)

The only combination that meets the requirements is A) 50 cookies and 30 muffins.