Question

The cost to rent a bike at the beach is $6.75 an hour plus an insurance fee of $15. Maria spent $48.75 when renting a bike on a recent trip to the beach. For how many hours did Mira rent the bike

Answer 1

Cost to rent a bike

STEP 1- Writing an equation

The total cost of the rent has two parts:

1. cost due to the hours of use: $6.75 per hour

2. insurance fee: $15

we have that the total cost is $48.75 and the insurance fee is $15

This is

$48.75=??+15$

We want to find the cost due to the time of use depends on the number of hours.

If she uses it for 1 hour, then the cost is $6.75

If she uses it for 2 hours, the cost is 2 · $6.75 = $13.5

If she uses it for 3 hours, the cost is 3 · $6.75 = $20.25

...

If she uses it x number of hours, the cost is x · $6.75 = $6.75x. Then,

Therefore, the equation we are going to use to find the number of hours, x, is:

$48.75=6.75x+15$

STEP 2 - Finding x

We want to solve the equation for x. This is "we want to leave x alone" on t¡one side of the equation

Substracting 15 both sides:

$\begin{gathered} 48.75=6.75x+15 \\ \downarrow \\ 48.75-15=6.75x+15-15 \\ 48.75-15=6.75x+(15-15) \\ 33.75=6.75x \end{gathered}$

Dividing by 6.75 both sides:

$\begin{gathered} 33.75=6.75x \\ \downarrow \\ \frac{33.75}{6.75}=\frac{6.75x}{6.75} \\ 5=x \end{gathered}$

Then, the number of hours, x is 5.

Answer: Maria rent the bike for 5 hours