What is 80% written as a decimal? Multiply that decimal by $q$ to get the daily charge for each additional day.

Add the cost for the first 3 days and the cost for the remaining 2 days, and set this sum equal to 230. Then solve the resulting one-variable equation.

In Desmos, type the expression 3x + 2*0.8x. This represents the total cost for 5 days as a function of the daily rate $x$.

On a new line, type y = 230. Then find the intersection of the graphs $y = 3x + 2\cdot 0.8x$ and $y = 230$. The x-value of this intersection is the company’s regular daily rental rate.

Sam rents the car for 5 days.

• For the first 3 days, the cost is $q$ dollars per day, so the cost is $3q$.
• For the remaining days, there are $5-3=2$ additional days.
• Each additional day costs 80% of $q$, which is $0.8q$ dollars per day.
• So the cost for the additional 2 days is $2\times 0.8q$.

The total charge for all 5 days is $230.

So, total cost = (cost for first 3 days) + (cost for next 2 days):

First simplify the expression involving $q$:

So the equation becomes:

Now solve $4.6q = 230$ by dividing both sides by $4.6$:

Compute the division:

• $4.6 \times 50 = 230$, so $\dfrac{230}{4.6} = 50$.

Therefore, the company’s regular daily rental rate is $50.