Question

Henry owns a food truck that sells tacos and burritos. He only has enough supplies to make 100 tacos or burritos. He sells each taco for $3 and each burrito for $5. Henry must sell no less than $360 worth of tacos and burritos each day. Also, he must sell no less than 20 tacos. If xx represents the number of tacos sold and yy represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
Number of Inequalities:
3
Inequality 1:
Select


Inequality 2:
Select


Inequality 3:
Select

Answer 1

Inequality 1:
x + y ≤ 100

Inequality 2:
3x + 5y ≥ 360

Inequality 3:
x ≥ 20

Graphical solution (description and vertices):
- Draw the line x + y = 100 (region is the area below/left of this line).
- Draw the line 3x + 5y = 360 (region is the area above/right of this line).
- Draw the vertical line x = 20 (region is to the right of this line).

The feasible region is the triangle bounded by the intersections of these lines. Solve the intersections:
- x = 20 and 3x + 5y = 360 → 60 + 5y = 360 → y = 60 → (20, 60)
- x = 20 and x + y = 100 → y = 80 → (20, 80)
- x + y = 100 and 3x + 5y = 360 → solve: 3x + 5(100 − x) = 360 → x = 70, y = 30 → (70, 30)

So the feasible region is the triangle with vertices (20, 60), (20, 80), and (70, 30).

One possible solution (inside the feasible region) is x = 50, y = 45:
- x + y = 95 ≤ 100
- 3x + 5y = 150 + 225 = 375 ≥ 360
- x = 50 ≥ 20

Thus (50, 45) is a valid solution.