Question

Ava and her children went into a movie theater where they sell drinks for $5.50 each and candies for $3 each. Ava has $45 to spend and must buy at least 10 drinks and candies altogether. If xx represents the number of drinks purchased and yy represents the number of candies purchased, write and solve a system of inequalities graphically and determine one possible solution.

a) Graphically solve the system of inequalities.
b) No solution is possible.
c) x = 10, y = 0
d) x = 0, y = 10

Answer 1

To solve the problem, set up a system of inequalities for Ava's spending and purchases. Graphically, these inequalities create a feasible region on a coordinate plane. One possible solution within this region is x = 10 and y = 0, which means Ava buys 10 drinks and no candies. So, the correct answer is c) x = 10, y = 0.

Step-by-step explanation:

To solve this problem, we need to set up a system of inequalities for Ava's spending and purchases.

Let xx represent the number of drinks purchased and yy represent the number of candies purchased.

We know that the price of a drink is $5.50 and the price of a candy is $3. Ava has $45 to spend, so the first inequality is: 5.50x + 3y ≤ 45.

We also know that Ava must buy at least 10 drinks and candies altogether, so the second inequality is: x + y ≥ 10.

Graphically, these two inequalities create a feasible region on a coordinate plane. One possible solution within this region is x = 10 and y = 0, which means Ava buys 10 drinks and no candies.

Therefore, the correct answer is c) x = 10, y = 0.