Suppose Meagan needs to drive the truck 10 miles to her new home.
a) What is the cost of using Truck A?
b) What is the cost of using Truck B?
c) Which company offers the better deal at this mileage?
2. Suppose Meagan needs to dive the truck 30 miles to her new home.
a) What is the cost of using Truck A?
b) What is the cost of using Truck B?
c) Which company offers the better deal at this mileage?
3. Suppose x = the number of miles the truck will be driven.
a) Write an algebraic expression representing the cost of Truck A.
b) Write an algebraic expression representing the cost of Truck B.
4. Suppose Meagan would like to know when the costs are equal between the two companies.
a) Write an equation that shows the costs are equal.
b) Solve the equation to find the mileage at which both companies charge the same amount.
5. Discuss how Meagan should make her decision based on these results.
Suppose Ryan wanted help with a problem, but didn't provide information on the cost of driving trucks.
Suppose also that he just dumped his problem on the tutors with no indication that he had done anything on his own to solve it.
What are the chances that he'll actually get any help?
(A) slim
(B) none
None especially from Steve!
a) To find the cost of using Truck A, we need to know the cost per mile for this truck.
b) To find the cost of using Truck B, we need to know the cost per mile for this truck.
c) To determine which company offers the better deal, we will compare the costs of using Truck A and Truck B for the given mileage.
2. a) To find the cost of using Truck A for a 30-mile distance, we need to know the cost per mile for this truck.
b) To find the cost of using Truck B for a 30-mile distance, we need to know the cost per mile for this truck.
c) To determine which company offers the better deal, we will compare the costs of using Truck A and Truck B for the given mileage.
3. a) The algebraic expression representing the cost of Truck A would be Cost of Truck A = (Cost per mile of Truck A) * x, where x represents the number of miles the truck will be driven.
b) The algebraic expression representing the cost of Truck B would be Cost of Truck B = (Cost per mile of Truck B) * x, where x represents the number of miles the truck will be driven.
4. a) The equation showing the costs are equal is (Cost per mile of Truck A) * x = (Cost per mile of Truck B) * x.
b) To solve the equation and find the mileage at which both companies charge the same amount, we can simplify the equation by canceling out the x factor on both sides: Cost per mile of Truck A = Cost per mile of Truck B. This will give us the equal mileage at which both companies charge the same amount.
5. Meagan should make her decision based on the costs of using Truck A and Truck B for the specific distance she needs to travel. By comparing the cost per mile for each truck, she can determine which company offers the better deal. It is important for her to consider not only the upfront costs but also any additional charges or conditions that may affect the overall cost. Meagan should also consider other factors such as the reputation and reliability of the companies, the condition of the trucks, and any additional services or benefits provided by each company.
To answer these questions, we need some information about the two truck companies and their pricing structures. Specifically, we need to know the cost per mile for each truck. Let's assume that Truck A charges $2 per mile and Truck B charges $3 per mile.
a) To find the cost of using Truck A for a 10-mile drive, we multiply the mileage by the cost per mile:
Cost of using Truck A = 10 miles * $2/mile = $20.
b) Similarly, to find the cost of using Truck B for a 10-mile drive:
Cost of using Truck B = 10 miles * $3/mile = $30.
c) Comparing the costs, we can see that Truck A is cheaper, so it offers a better deal for a 10-mile drive.
Now let's move on to the scenario where Meagan needs to drive 30 miles.
a) Cost of using Truck A = 30 miles * $2/mile = $60.
b) Cost of using Truck B = 30 miles * $3/mile = $90.
c) Again, looking at the costs, Truck A is cheaper and offers a better deal for a 30-mile drive.
For the third set of questions, we'll use algebraic expressions to represent the costs of the trucks.
Let x be the number of miles the truck will be driven.
a) Algebraic expression representing the cost of Truck A: Cost = $2/mile * x = $2x.
b) Algebraic expression representing the cost of Truck B: Cost = $3/mile * x = $3x.
Moving on to the fourth set of questions, we need to find the mileage at which both companies charge the same amount.
a) Equation showing the costs are equal: $2x = $3x.
b) To solve the equation, we subtract $2x from both sides: $3x - $2x = $0.
Simplifying, we get x = $0, which means there is no mileage at which both companies charge the same amount. This suggests that the costs are never equal.
Finally, let's discuss how Meagan should make her decision based on these results.
Based on the calculations, Truck A is cheaper than Truck B per mile. So, for shorter distances, Truck A offers a better deal. However, if the mileage increases significantly, Truck B becomes more expensive.
Meagan should evaluate the distance she needs to drive and consider her budget. If the distance is relatively short, choosing Truck A would be more cost-effective. On the other hand, if the distance is long, she might want to consider the convenience or other factors offered by Truck B, despite the higher cost per mile.