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 \( h \).
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Rearrange the equation to isolate \( h \): \[ 92h - 78h = 250 - 180 \]
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Simplify both sides: \[ 14h = 70 \]
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Divide both sides by 14: \[ h = \frac{70}{14} = 5 \]
Thus, the two companies will charge the same amount when renting for 5 hours.