Question

Two shops rent kayaks for a rental fee plus a fee per hour. How many hours must a kayak be rented forthe total costs to be the same?

Shop A
Rental fee: $2
Hourly fee: $7


Shop B
Rental fee: $5
Hourly fee: $6

(1 point)
The total costs are the same when a kayak is rented for
hours

Answer 1

To find the number of hours at which the total costs for both shops are the same, we can set up equations for the total costs.

Let \( h \) be the number of hours the kayak is rented.

For Shop A:
- Total cost \( C_A = 2 + 7h \)

For Shop B:
- Total cost \( C_B = 5 + 6h \)

We want to find when the total costs are equal, so we set the two equations equal to each other:

\[
2 + 7h = 5 + 6h
\]

Now, we'll solve for \( h \).

1. Subtract \( 6h \) from both sides:

\[
2 + 7h - 6h = 5
\]

This simplifies to:

\[
2 + h = 5
\]

2. Subtract 2 from both sides:

\[
h = 5 - 2
\]

So,

\[
h = 3
\]

Thus, the total costs are the same when a kayak is rented for **3 hours**.