Question

The local basketball team is raising money by selling coupon books for $25 each and popcorn buckets for $15 each. They want to raise at least $450 and can sell up to 300 items. Which solution(s) are valid within this context?

A) x = 10, y = 20
B) x = 20, y = 10
C) x = 18, y = 12
D) x = 15, y = 10

Answer 1

The valid solutions within this context are: A) x = 10, y = 20, B) x = 20, y = 10, C) x = 18, y = 12, and D) x = 15, y = 10.

Step-by-step explanation:

In order to find the valid solution(s) within this context, we need to consider the constraints given. The local basketball team wants to raise at least $450 and can sell up to 300 items. Let x be the number of coupon books sold and y be the number of popcorn buckets sold. The cost of each coupon book is $25 and the cost of each popcorn bucket is $15. Therefore, the total amount raised can be represented as:

25x + 15y ≥ 450

Additionally, the total number of items sold cannot exceed 300, so:

x + y ≤ 300

Now, let's evaluate each solution option:

• A) x = 10, y = 20: The total amount raised would be 25(10) + 15(20) = $500, which is greater than or equal to $450. The total number of items sold is 10 + 20 = 30, which is less than or equal to 300. This is a valid solution option.
• B) x = 20, y = 10: The total amount raised would be 25(20) + 15(10) = $650, which is greater than or equal to $450. The total number of items sold is 20 + 10 = 30, which is less than or equal to 300. This is a valid solution option.
• C) x = 18, y = 12: The total amount raised would be 25(18) + 15(12) = $690, which is greater than or equal to $450. The total number of items sold is 18 + 12 = 30, which is less than or equal to 300. This is a valid solution option.
• D) x = 15, y = 10: The total amount raised would be 25(15) + 15(10) = $575, which is greater than or equal to $450. The total number of items sold is 15 + 10 = 25, which is less than or equal to 300. This is a valid solution option.

Therefore, options A, B, C, and D are all valid solutions within this context.