Question

Joe and Peter go to the fair on Tuesday. They buy 8 pretzels and 8 nachos and spend no more than $40. On Thursday, they return to the fair and purchase 2 pretzels and 5 nachos and spend no more than $20. Write the inequalities and graph the solution.

a) 8x + 8y ≤ 40; 2x + 5y ≤ 20
b) 8x + 8y ≥ 40; 2x + 5y ≥ 20
c) 8x + 8y < 40; 2x + 5y < 20
d) 8x + 8y > 40; 2x + 5y > 20

Answer 1

The correct answer is a) 8x + 8y ≤ 40; 2x + 5y ≤ 20. To graph the solution, plot the inequalities on a coordinate plane and shade the region that satisfies both inequalities.

Step-by-step explanation:

The correct answer is: a) 8x + 8y ≤ 40; 2x + 5y ≤ 20.

To write the inequalities, we need to determine the maximum amount spent on pretzels and nachos on Tuesday and Thursday. Let x represent the number of pretzels and y represent the number of nachos.

On Tuesday, they spent no more than $40, so 8x (cost of pretzels) + 8y (cost of nachos) ≤ 40.

On Thursday, they spent no more than $20, so 2x (cost of pretzels) + 5y (cost of nachos) ≤ 20.

To graph the solution, we can plot these inequalities on a coordinate plane and shade the region that satisfies both inequalities. The shaded region represents the possible combinations of pretzels and nachos they can buy without exceeding their budget.