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.

Question

Which point represents a viable solution?

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Group of answer choices

(6, –2)

(2, 12)

(12, 4)

(8, 9)

Answer 1

To determine which point represents a viable solution to the given scenario, we need to check each candidate point against the constraints:

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

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

Now, let's evaluate each point:

1. (6, –2):

   • Check if \( x + y \leq 15 \): \[ 6 + (-2) = 4 \leq 15 \] (True)
   • Check if \( x \leq 6 \): \[ 6 \leq 6 \] (True)
   • However, y is negative, which isn't possible in this context. Not viable.

2. (2, 12):

   • Check if \( x + y \leq 15 \): \[ 2 + 12 = 14 \leq 15 \] (True)
   • Check if \( x \leq 6 \): \[ 2 \leq 6 \] (True)
   • This point satisfies both constraints. Viable solution.

3. (12, 4):

   • Check if \( x + y \leq 15 \): \[ 12 + 4 = 16 \leq 15 \] (False)
   • Does not satisfy the first constraint. Not viable.

4. (8, 9):

   • Check if \( x + y \leq 15 \): \[ 8 + 9 = 17 \leq 15 \] (False)
   • Does not satisfy the first constraint. Not viable.

Based on this evaluation, the point that represents a viable solution is (2, 12).