Question

Sherry just got her pilots license and wants to rent a plane platinum plane company charges $180 plus $92 per hour to rent a plane the plastic plane company charges $250 plus $78 per hour for what number of hours with the company charge the same amount

Answer 1

To find the number of hours at which the charges from both companies are the same, we can set up an equation based on the given costs from each company.

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

**Platinum Plane Company:**
The cost is given by:
\[
\text{Cost}_{\text{Platinum}} = 180 + 92h
\]

**Plastic Plane Company:**
The cost is given by:
\[
\text{Cost}_{\text{Plastic}} = 250 + 78h
\]

We want to find the number of hours \( h \) where the costs are equal:
\[
180 + 92h = 250 + 78h
\]

Now, we will solve for \( h \).

1. Rearrange the equation to isolate \( h \):
\[
92h - 78h = 250 - 180
\]

2. Simplify both sides:
\[
14h = 70
\]

3. Divide both sides by 14:
\[
h = \frac{70}{14} = 5
\]

Thus, the two companies will charge the same amount when renting for **5 hours**.

Answer 2

What would the charge be for that number of hours?

Answer 3

To find the charge for 5 hours at either company, we can calculate the cost using the formulas we derived earlier.

**Platinum Plane Company:**
\[
\text{Cost}_{\text{Platinum}} = 180 + 92h
\]
Substituting \( h = 5 \):
\[
\text{Cost}_{\text{Platinum}} = 180 + 92 \times 5 = 180 + 460 = 640
\]

**Plastic Plane Company:**
\[
\text{Cost}_{\text{Plastic}} = 250 + 78h
\]
Substituting \( h = 5 \):
\[
\text{Cost}_{\text{Plastic}} = 250 + 78 \times 5 = 250 + 390 = 640
\]

Both companies will charge **$640** for 5 hours of rental.