Question
Write and solve a system of equations. Only write the number, not the word days
At ZIppy rent a car, you can rent a car for 25$ per day, which a one time free of 100$. At Speedy rent a car, you can rent a car for 30$ per day, with a one time fee of 30$ Write and solve a system of equations to find the number of days for which both car rental locations will cost the same.
At ZIppy rent a car, you can rent a car for 25$ per day, which a one time free of 100$. At Speedy rent a car, you can rent a car for 30$ per day, with a one time fee of 30$ Write and solve a system of equations to find the number of days for which both car rental locations will cost the same.
Answers
GPT-4o mini
Let \( x \) represent the number of days you rent the car.
For Zippy Rent a Car, the total cost (\( C_1 \)) can be expressed as:
\[
C_1 = 25x + 100
\]
For Speedy Rent a Car, the total cost (\( C_2 \)) can be expressed as:
\[
C_2 = 30x + 30
\]
To find the number of days for which both rental locations will cost the same, we set the two equations equal to each other:
\[
25x + 100 = 30x + 30
\]
Now, we can solve for \( x \):
1. Subtract \( 25x \) from both sides:
\[
100 = 5x + 30
\]
2. Subtract 30 from both sides:
\[
70 = 5x
\]
3. Divide both sides by 5:
\[
x = 14
\]
Thus, the number of days for which both car rental locations will cost the same is 14. The solution is \( x = 14 \).
For Zippy Rent a Car, the total cost (\( C_1 \)) can be expressed as:
\[
C_1 = 25x + 100
\]
For Speedy Rent a Car, the total cost (\( C_2 \)) can be expressed as:
\[
C_2 = 30x + 30
\]
To find the number of days for which both rental locations will cost the same, we set the two equations equal to each other:
\[
25x + 100 = 30x + 30
\]
Now, we can solve for \( x \):
1. Subtract \( 25x \) from both sides:
\[
100 = 5x + 30
\]
2. Subtract 30 from both sides:
\[
70 = 5x
\]
3. Divide both sides by 5:
\[
x = 14
\]
Thus, the number of days for which both car rental locations will cost the same is 14. The solution is \( x = 14 \).