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.

Question

Let x=
number of games and y=
number of snacks. Which of the following sets of inequalities represents this situation?

(1 point)
Responses

x+y≥12

3x+4y≥40

x plus y is greater than or equal to 12 3 x plus 4 y is greater than or equal to 40

x+y≤12

3x+4y≤40

x plus y is less than or equal to 12 3 x plus 4 y is less than or equal to 40

x+y≥12

3x+4y≤40

x plus y is greater than or equal to 12 3 x plus 4 y is less than or equal to 40

3x+4y≥12

x+y≤40

3 x plus 4 y is greater than or equal to 12 x plus y is less than or equal to 40

Answer 1

To represent the situation with inequalities, we need to consider the two constraints given:

1. Neal has a budget of $40 to spend on games and snacks.
2. Neal wants to buy at least 12 items total, consisting of games and snacks.

Let's set up the inequalities based on these conditions.

• Let \( x \) be the number of games Neal buys, where each game costs $3.
• Let \( y \) be the number of snacks Neal buys, where each snack costs $4.

For the budget constraint: Since Neal is spending $3 on each game and $4 on each snack, the total cost can be expressed as: \[ 3x + 4y \leq 40 \]

For the total items constraint: He wants to buy at least 12 items in total, so we have: \[ x + y \geq 12 \]

Putting these together, the correct set of inequalities representing Neal's situation is:

1. \( x + y \geq 12 \)
2. \( 3x + 4y \leq 40 \)

Thus, the correct response is: x + y ≥ 12 and 3x + 4y ≤ 40.