You need to rent a moving truck for two days. Rider Moving Trucks charges $50 per day and $.50 per mile. UMove Trucks charges $45 per day and $0.75 per mile. Write an equation describing each situation. Graph them on the same xy axis. You only need Quadrant I because all values are positive. The x axis represents mileage. Use a scale of 0 to 100 counting by 10’s. The y axis is cost and goes from $0 to $160, counting by 20’s.
a. From your graph, after how many miles would the trucks cost the same?
b. Which company will give you a better deal if you drive less than 30 miles?
c. Which company will give you a better deal if you drive more than 60 miles?
Rider:
y = .5x + 50
UMove:
y = .75x + 45
Just follow the instructions, they are quite clear.
To write the equations describing each situation, we can start with the equation for Rider Moving Trucks:
Equation 1: Cost of Rider Moving Trucks = 50 * number of days + 0.50 * number of miles
Similarly, for UMove Trucks:
Equation 2: Cost of UMove Trucks = 45 * number of days + 0.75 * number of miles
Now, let's graph these equations on the same xy-axis as given in the question.
On the x-axis, we have the mileage ranging from 0 to 100, counting by 10's. On the y-axis, we have the cost ranging from $0 to $160, counting by 20's.
a. To find the number of miles at which the trucks cost the same, we need to find the point at which the two equations intersect on the graph. The x-coordinate of that point will represent the number of miles at which the cost is the same for both companies.
b. To determine which company will give a better deal if you drive less than 30 miles, we need to compare the cost for driving less than 30 miles using both equations. We can do this by substituting x = 30 into each equation and comparing the resulting costs.
c. To figure out which company will give a better deal if you drive more than 60 miles, we need to compare the cost for driving more than 60 miles using both equations. Again, we can substitute x = 60 into each equation and compare the resulting costs.
By graphing the two equations and analyzing the points where they intersect, as well as evaluating the costs for specific mileage values, we can answer the questions about the moving truck rentals.