Question

A rental car company charges $37.50 per day to rent a car and $0.05 for every mile driven. Alyssa wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $200 to spend.

write a equations streched out

Answer 1

To express Alyssa's car rental costs using an equation, we need to account for both the daily rental fee and the mileage charges.

1. **Cost of renting the car per day**: $37.50
2. **Cost per mile driven**: $0.05
3. **Miles she plans to drive**: 100 miles
4. **Total budget**: $200

Now let's break down the total cost and formulate the equation:

- The cost to rent the car for one day is a flat fee of $37.50.
- The cost for driving 100 miles will be calculated as $0.05 per mile multiplied by the total miles driven:

\[
\text{Cost for miles} = 0.05 \times \text{miles driven} = 0.05 \times 100
\]

- Therefore, the mileage cost is:

\[
\text{Cost for miles} = 0.05 \times 100 = 5
\]

Combining these costs, the total cost (C) that Alyssa will incur from renting the car can be expressed as follows:

\[
C = \text{Cost of rental} + \text{Cost for miles}
\]

Substituting the values into the equation, we have:

\[
C = 37.50 + 5
\]

This total cost needs to be less than or equal to her budget of $200:

\[
C \leq 200
\]

Now substituting the earlier expression for total cost \(C\):

\[
37.50 + 5 \leq 200
\]

This can be simplified to:

\[
42.50 \leq 200
\]

Finally, we can conclude that under her planned usage, Alyssa's rental car expense will comfortably fall within her budget. To summarize:

1. The cost equation is:
\[
C = 37.50 + (0.05 \times 100)
\]

2. The budget constraint is:
\[
C \leq 200
\]

It's clear that Alyssa can afford the rental car under her given conditions.