Question 8 of 10

Question

A basket holds at most 15 pounds of apples and oranges. There are no more than 6 pounds of apples in the basket. This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges.
Which point represents a viable solution?
A. (2,12)
в. (8,9)
C. (12,4)
D. (6, -2)

Answer 1

To determine which point among the options represents a viable solution for the weight of apples (x) and oranges (y), we need to consider the constraints given in the scenario:

1. The total weight of apples and oranges cannot exceed 15 pounds: \[ x + y \leq 15 \]

2. The weight of the apples cannot exceed 6 pounds: \[ x \leq 6 \]

Now, let's evaluate each of the points provided:

A. (2, 12)

• \(x + y = 2 + 12 = 14 \leq 15\) (satisfied)
• \(x = 2 \leq 6\) (satisfied)
• Viable solution

B. (8, 9)

• \(x + y = 8 + 9 = 17\) (not satisfied)
• Not a viable solution

C. (12, 4)

• \(x + y = 12 + 4 = 16\) (not satisfied)
• Not a viable solution

D. (6, -2)

• \(x + y = 6 + (-2) = 4 \leq 15\) (satisfied)
• \(x = 6 \leq 6\) (satisfied)
• However, weight cannot be negative (y = -2 is not realistic).
• Not a viable solution

Based on this analysis, the only point that meets all the criteria without any issues is A. (2, 12).