Question

Katie is buying plates & mugs. She wants to buy at least 8 items. What are the possibilities if plates cost $8, mugs cost $7, and she plans to spend less than $12 on each item?

a. 2 plates, 6 mugs
b. 1 plate, 7 mugs
c. 3 plates, 5 mugs
d. 4 plates, 4 mugs

Answer 1

To solve this problem, we can create equations based on the given information. By solving the equations and inequalities, we find that the only possibility is 4 plates and 4 mugs.

Step-by-step explanation:

To solve this problem, we can create equations based on the given information. Let x represent the number of plates and y represent the number of mugs Katie wants to buy. We are given the following information:

1. 
   
3. Plates cost $8, so the cost of plates is 8x.
4. 
   
6. Mugs cost $7, so the cost of mugs is 7y.
7. 
   
9. Katie plans to spend less than $12 on each item, so we have two inequalities: 8x < 12 and 7y < 12.
10. 
    
12. Katie wants to buy at least 8 items, so we have the inequality x + y >= 8.

Solving these inequalities, we find that the only possibility is 4 plates and 4 mugs. Therefore, the answer is option d: 4 plates, 4 mugs.