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?
1st step: write a function for each company. For example,
Rider: y = 50 + 0.50x
now what?
To write equations for each situation, let's define the variables:
- x: mileage (in miles)
- y1: cost from Rider Moving Trucks (in dollars)
- y2: cost from UMove Trucks (in dollars)
a. The equation for Rider Moving Trucks can be written as:
y1 = 50 + 0.50x
Similarly, the equation for UMove Trucks is:
y2 = 45 + 0.75x
b. To determine when the trucks cost the same, we need to set the two equations equal to each other and solve for x:
50 + 0.50x = 45 + 0.75x
To simplify, let's move all the terms with x to one side:
0.25x = 5
Dividing both sides by 0.25, we get:
x = 5 / 0.25
x = 20
Therefore, after 20 miles, the trucks will cost the same.
c. To find out which company is a better deal based on the mileage, we need to compare their costs for different values of x.
For mileage less than 30 miles:
For Rider Moving Trucks:
y1 = 50 + 0.50 * 30
y1 = 50 + 15
y1 = 65 dollars
For UMove Trucks:
y2 = 45 + 0.75 * 30
y2 = 45 + 22.5
y2 = 67.5 dollars
Therefore, if you drive less than 30 miles, Rider Moving Trucks is the better deal.
For mileage more than 60 miles:
For Rider Moving Trucks:
y1 = 50 + 0.50 * 60
y1 = 50 + 30
y1 = 80 dollars
For UMove Trucks:
y2 = 45 + 0.75 * 60
y2 = 45 + 45
y2 = 90 dollars
Therefore, if you drive more than 60 miles, Rider Moving Trucks is the better deal.