Steven is moving to another city next weekend and wants to rent a moving truck. The rental rates for two companies in his area are shown below. Each company charges an initial fee for renting the truck, plus an additional amount per mile.
Company 1:
Miles: 30 Rental Charge: $53.55
Miles: 60 Rental Charge: $87.15
Miles: 90 Rental Charge: $120.75
Miles: 120 Rental Charge: $154.35
Miles: 150 Rental Charge: $187.35
Company 2:
Miles: 25 Rental Charge: $56.75
Miles: 50 Rental Charge: $78.00
Miles: 75 Rental Charge: $99.25
Miles: 100 Rental Charge: $120.50
Miles: 125 Rental Charge: $141.75
I am looking to find the initial charge so that I can then find additional amount per mile. I have come up with the equation of 30x + y = 53.55 but am unsure of where to go next.
Company 1 Company 2
Mileage Rate Mileage Rate
30 53.55 $33.60 $19.95 Initial Fee (87.15-53.55=33.60) 25 $56.75 $21.25 $35.50 Initial Fee (78-56.75=21.25)
60 87.15 $33.60 50 $78.00 $21.25
90 120.75 $33.60 75 $99.25 $21.25
120 154.35 $33.60 100 $120.50 $21.25
150 187.95 $33.60 125 $141.75 $21.25
Rate Company 1 $1.12 Rate Company 2 $0.85
33.60/30 21.25/25
85 millas x 1.12 = $95.20 85 millas x .85= $72.25 $22.95
Initial Fee $19.95 $35.50
Total $115.15 Total $107.75 $7.40
Compania 2 es mas barata que la Compania 1 por $7.40
To find the initial charge for renting the truck, you can use the information given for each company and set up a system of equations.
Let's assume the initial charge for Company 1 is 'x' and the additional amount per mile is 'y'.
From the information provided, we can set up the following equation for Company 1:
30x + 30y = 53.55 ---(equation 1)
Similarly, for Company 2:
25x + 25y = 56.75 ---(equation 2)
Now, you can solve this system of equations to find the initial charge.
To find the initial charge for renting the truck and the additional amount per mile for each company, we can use the information given and solve a system of equations.
Let's use the equation you mentioned for Company 1: 30x + y = 53.55. Here, x represents the additional amount per mile and y represents the initial charge.
Now, let's set up a similar equation for Company 2. Let's consider the first data point for Company 2, where the rental charge is $56.75 for 25 miles. We can set up the equation: 25x + y = 56.75.
So, we now have a system of equations:
Equation 1: 30x + y = 53.55
Equation 2: 25x + y = 56.75
To solve this system of equations, we can use any method such as substitution or elimination. One straightforward method is to subtract Equation 2 from Equation 1:
(30x + y) - (25x + y) = 53.55 - 56.75
5x = -3.20
Now, divide both sides of the equation by 5 to solve for x:
5x/5 = -3.20/5
x = -0.64
So, the additional amount per mile for both companies is -0.64.
To find the initial charge (y) for each company, we can substitute the value of x = -0.64 into either Equation 1 or Equation 2. Let's use Equation 1:
30x + y = 53.55
30(-0.64) + y = 53.55
-19.2 + y = 53.55
y = 53.55 + 19.2
y ≈ 72.75
Therefore, for Company 1, the initial charge (y) is approximately $72.75.
To find the initial charge for Company 2, you can substitute the value of x = -0.64 into Equation 2:
25x + y = 56.75
25(-0.64) + y = 56.75
-16 + y = 56.75
y = 56.75 + 16
y = 72.75
Hence, the initial charge (y) for Company 2 is also $72.75.
To summarize:
- Company 1 has an initial charge of $72.75 and an additional charge of -0.64 per mile.
- Company 2 also has an initial charge of $72.75 and an additional charge of -0.64 per mile.
60x + y = 87.15
subtracting equations
... 30x = 33.60
substituting
... 33.60 + y = 53.55
... y = 19.95