A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost, ƒ(m) is a function of the number of miles, m, that the car is driven. In addition to a flat fee of $75, Plan A offers a rate of $0.20 per mile for an unlimited number of miles. Plan B offers a higher mileage rate of $0.35 per mile but does not charge a flat fee for the rental. Create a system of linear functions modeling the cost of the car rental plans, A and B, as a function of the miles driven. For how many miles, m, will the rental fee be the same under both plans A and B?

System of lynear functions:

Plan A: f(m) = 0.20m+75

Plan B: f(m) = 0.35m

Where m, is the number of driven miles.

The rental fee is the same for m = 500 miles

Step-by-step explanation:

We know that plan A offers a rate of $0.20 per mile and a flat fee of $75, so for plan A the function f(m) is defined as:

f(m)=0.20m+75

As we see, if we drive zero miles, the plan A cost $75, which is the flat fee, as the problem says.

We also know plan B offer a rate of $0.35 per miles without any flat fee. So for the plan B the function f(m) is defined as:

f(m)=0.35m

Finally, we need to know for how many miles will the rental fee be the same under both plans A and B. Then, we need to match the functions for plan A and plan B, and clear the value of m:

0.20m + 75 = 0.35m

75 = 0.35m - 0.20m

75 = 0.15m

m = 75/0.15

m = 500 miles

We can probe this result replacing the value of m in both equations, and we obtain that:

For plan A:

f(m=500 miles)=(0.20$/mile)(500miles) + $75

f(m=500 miles)= $175

For plan B:

f(m=500 miles)=(0.35$/mile)(500miles)

f(m=500 miles)= $175