Question

William and his children went into a restaurant that sells hamburgers for $8 each and drinks for $2.50 each. William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether. If xx represents the number of hamburgers purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

Answer: We can set up the following system of inequalities to represent the situation:

8x + 2.5y <= 95 (the total cost of the hamburgers and drinks must be less than or equal to $95)

x >= 18-y (William must buy no less than 18 hamburgers and drinks altogether)

x >= 0, y >= 0 (non-negative values for the number of hamburgers and drinks purchased)

To graph the system of inequalities, we can start by graphing the inequality 8x + 2.5y <= 95, which represents a boundary line in the xy-plane. Since it's a less or equal sign, we will shade the area that is below the line.

The second inequality represents a boundary line which is the line x = 18-y. Since x must be greater than or equal to 18-y, we will shade the area that is on or above the line.

The third inequality is a non-negative constraint for both x and y, so we will graph the x and y axis and shade the area that is above them.

After combining all the shaded areas, we'll get a feasible solution region that represents possible values of x and y that satisfies the system of inequalities.

One possible solution to the system of inequalities is x=24 and y=6, which is a point in the feasible region that satisfies all the inequalities.

It's worth noting that there could be other solutions as well, depending on the number of hamburgers and drinks William wants to buy.

Explanation: