Question

Juan and his children went into a restaurant where they sell drinks for $2 each and tacos for $4 each. Juan has $40 to spend and must buy a minimum of 11 drinks and tacos altogether. If xx represents the number of drinks purchased and yy represents the number of tacos purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

A system of inequalities is set up to determine the combinations of drinks and tacos Juan can buy: 2x + 4y <= 40 for the budget constraint and x + y >= 11 for the minimum items constraint. Graphing these inequalities allows finding a solution such as 7 drinks and 4 tacos, which meets both constraints.

Step-by-step explanation:

To solve Juan's problem, we need to write and solve a system of inequalities. Given that drinks cost $2 each and tacos cost $4 each, and Juan has $40 to spend, we can express the cost constraint with the inequality:

2x + 4y ≤ 40

Additionally, we need to satisfy the minimum number of 11 drinks and tacos combined which gives us another inequality:

x + y ≥ 11

Now let's graph these inequalities. The intersection of these constraints on the graph will give us the feasible region. Let's choose one possible point from within this feasible region as a solution, keeping in mind that x and y must be whole numbers as they represent the number of drinks and tacos respectively. For instance, if x=7 drinks and y=4 tacos, then this solution meets both constraints:

2(7) + 4(4) = 14 + 16 = 30 ≤ 40

and

7 + 4 = 11 ≥ 11

This is one possible solution where Juan spends $30 and buys a total of 11 drinks and tacos.