Let's analyze each question one at a time.
17.
We have the inequalities:
- \(15x + 5y \leq 1000\)
- \(2x + y \leq 50\)
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:
- \(3c + 5m \geq 300\)
- \(c + m \leq 80\)
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.