Create a system of linear equations with this situation:
Megan considers two different car rental options. One option costs $19 per day plus $0.12 per kilometre . Another option costs $42.50 per day for unlimited kilometres .
Thanks :)
19 + .12x = 42.5
.12x = 23.5
x = 195.83
Thank u so much:)
To create a system of linear equations for this situation, we will need to define some variables.
Let's say:
- x is the number of days Megan rents the car.
- y is the total cost in dollars for the first option (cost per day plus cost per kilometer).
- z is the total cost in dollars for the second option (flat rate per day for unlimited kilometers).
Now, let's derive the equations based on the given information:
For the first option:
- The cost per day is $19, so the cost for the number of days x will be 19x.
- The cost per kilometer is $0.12, so the cost for the number of kilometers traveled is 0.12y. However, we don't know the number of kilometers Megan will travel, so we'll have to introduce another variable k to represent the number of kilometers. Therefore, the cost based on the number of kilometers traveled will be 0.12k.
- Combining these costs, the total cost for the first option (y) will be: y = 19x + 0.12k.
For the second option:
- The cost per day is a flat rate of $42.50, which means it does not depend on the number of days (x) or kilometers traveled (k): z = 42.50.
So, the system of linear equations representing Megan's car rental options is:
Equation 1: y = 19x + 0.12k
Equation 2: z = 42.50
In these equations, x represents the number of days rented, y represents the total cost for the first option, and z represents the total cost for the second option.