Question: 09/09-10/26 Bell Ringer The Food Truck Showdown Scenario Taco Trek charges a flat $4 delivery fee plus $3 per taco. Burrito Bus charges a flat $10 delivery fee plus $1.50 per taco. Task 1. Write an equation comparing the total cost of ordering $t$ tacos from both food trucks when the costs are equal. 2. Solve the equation to find how many tacos you need to order for both trucks to cost the exact same amount. 3. If your study group wants to order 6 tacos, which food truck should you order from to save money? Show your math.

1. **State the problem:** We want to compare the total cost of ordering $t$ tacos from Taco Trek and Burrito Bus and find when their costs are equal. 2. **Write the cost equations:** - Taco Trek cost: $$C_1 = 4 + 3t$$ - Burrito Bus cost: $$C_2 = 10 + 1.5t$$ 3. **Set the costs equal to find $t$: $$4 + 3t = 10 + 1.5t$$** 4. **Solve the equation:** $$4 + 3t = 10 + 1.5t$$ Subtract $1.5t$ from both sides: $$4 + \cancel{3t} - \cancel{1.5t} = 10 + \cancel{1.5t} - \cancel{1.5t}$$ $$4 + 1.5t = 10$$ Subtract 4 from both sides: $$4 - 4 + 1.5t = 10 - 4$$ $$1.5t = 6$$ Divide both sides by 1.5: $$\frac{\cancel{1.5}t}{\cancel{1.5}} = \frac{6}{1.5}$$ $$t = 4$$ 5. **Interpretation:** Ordering 4 tacos makes the total cost the same for both food trucks. 6. **Compare costs for 6 tacos:** - Taco Trek: $$4 + 3(6) = 4 + 18 = 22$$ - Burrito Bus: $$10 + 1.5(6) = 10 + 9 = 19$$ 7. **Conclusion:** For 6 tacos, Burrito Bus is cheaper by $$22 - 19 = 3$$. **Final answer:** - Equation: $$4 + 3t = 10 + 1.5t$$ - Equal cost at $$t = 4$$ tacos - For 6 tacos, order from Burrito Bus to save money.