Question

Neal takes $40 to the festival to spend on games and snacks. The games cost $3 each, and the snacks cost $4 each. Neal would like to be able to play and purchase at least 12 things.%0D%0A%0D%0ALet x= number of games and y= number of snacks. Which of the following sets of inequalities represents this situation?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A3x+4y≥12%0D%0A%0D%0Ax+y≤40%0D%0A%0D%0A3 x plus 4 y is greater than or equal to 12 x plus y is less than or equal to 40%0D%0A%0D%0Ax+y≤12%0D%0A%0D%0A3x+4y≤40%0D%0A%0D%0Ax plus y is less than or equal to 12 3 x plus 4 y is less than or equal to 40%0D%0A%0D%0Ax+y≥12%0D%0A%0D%0A3x+4y≤40%0D%0A%0D%0Ax plus y is greater than or equal to 12 3 x plus 4 y is less than or equal to 40%0D%0A%0D%0Ax+y≥12%0D%0A%0D%0A3x+4y≥40

Answer 1

To analyze the situation, let's break it down into inequalities based on Neal's constraints:

1. **Cost Constraint**: Neal has $40 to spend. The games cost $3 each (x games) and snacks cost $4 each (y snacks). Therefore, the total cost inequality can be expressed as:
\[
3x + 4y \leq 40
\]

2. **Quantity Constraint**: Neal wants to play and purchase at least 12 items (games and snacks combined). Therefore, the total number of items inequality can be expressed as:
\[
x + y \geq 12
\]

So the correct set of inequalities representing the situation is:
1. \(3x + 4y \leq 40\)
2. \(x + y \geq 12\)

Looking at the options you provided, the correct one appears to be:
**3 x + 4 y ≤ 40 and x + y ≥ 12**.