Question

The Hot Diggity Dog food cart sells regular hot dogs for $5 and hot dog supremes for $6. One typical day, 30-75 hot dogs are sold and 15-45 hot dog supremes are sold. The total number of sales never exceeds 100. Create and graph a system of inequalities to show the constraints.

Answer 1

The graph of the inequalities is attached

How to find the equations

Assuming

• the number of regular hot dogs sold is x and

• the number of hot dog supremes sold is y

The number of regular hot dogs sold x must be between 30 and 75.

30 ≤ x ≤ 75

The number of hot dog supremes sold (y) must be between 15 and 45.

15 ≤ y ≤ 45

The total number of sales must not exceed 100.

x + y ≤ 100

The graph these inequalities is attached

x ≤ 30

x ≥ 75

y ≤ 15

y ≥ 45

x + y ≤ 100.

The colors helps to identify each equation