Question
Who wants to rent a car rental car company charges $35 per day plus $.10 per mile driven rental company be charges $25 per day plus $.15 per mile driven how many miles driven will the price charge by each company be the same miles
Answers
GPT-4o mini
Let's denote \( x \) as the number of miles driven.
For the first car rental company, the total cost \( C_1 \) can be expressed as:
\[
C_1 = 35 + 0.10x
\]
For the second car rental company, the total cost \( C_2 \) is:
\[
C_2 = 25 + 0.15x
\]
To find the mileage at which both companies charge the same amount, we set the two equations equal to each other:
\[
35 + 0.10x = 25 + 0.15x
\]
Now, we can solve for \( x \). First, isolate the \( x \) terms on one side:
\[
35 - 25 = 0.15x - 0.10x
\]
\[
10 = 0.05x
\]
Next, solve for \( x \) by dividing both sides by 0.05:
\[
x = \frac{10}{0.05}
\]
\[
x = 200
\]
Therefore, the price charged by each company will be the same when \( 200 \) miles have been driven.
For the first car rental company, the total cost \( C_1 \) can be expressed as:
\[
C_1 = 35 + 0.10x
\]
For the second car rental company, the total cost \( C_2 \) is:
\[
C_2 = 25 + 0.15x
\]
To find the mileage at which both companies charge the same amount, we set the two equations equal to each other:
\[
35 + 0.10x = 25 + 0.15x
\]
Now, we can solve for \( x \). First, isolate the \( x \) terms on one side:
\[
35 - 25 = 0.15x - 0.10x
\]
\[
10 = 0.05x
\]
Next, solve for \( x \) by dividing both sides by 0.05:
\[
x = \frac{10}{0.05}
\]
\[
x = 200
\]
Therefore, the price charged by each company will be the same when \( 200 \) miles have been driven.
What will the price be for you that number of miles
GPT-4o mini
To find the price for both rental companies at 200 miles driven, we can substitute \( x = 200 \) into the cost equations for each company.
### For the first rental company:
\[
C_1 = 35 + 0.10 \times 200
\]
\[
C_1 = 35 + 20
\]
\[
C_1 = 55
\]
### For the second rental company:
\[
C_2 = 25 + 0.15 \times 200
\]
\[
C_2 = 25 + 30
\]
\[
C_2 = 55
\]
Thus, the price charged by each company when driving 200 miles will be **$55**.
### For the first rental company:
\[
C_1 = 35 + 0.10 \times 200
\]
\[
C_1 = 35 + 20
\]
\[
C_1 = 55
\]
### For the second rental company:
\[
C_2 = 25 + 0.15 \times 200
\]
\[
C_2 = 25 + 30
\]
\[
C_2 = 55
\]
Thus, the price charged by each company when driving 200 miles will be **$55**.
Related Questions
Alex needs to rent a minivan for a week to take his band on tour.
Easyvans charges $230 plus $0.10/...
Joseph is going on a trip and he needs to rent a car. He looks online and finds two companies that o...
Joseph is going on a trip and he needs to rent a car. He looks online and finds two companies that o...
Rental Company A charges a fee of $80 plus $35 per day to rent a mid-sized car. Rental Company B cha...