Renting an electric cart

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Question from Desiree, a student:

Vacation Rentals rents electric carts for travel on their grounds. The economy plan rents
carts for $\$26$ per day and the premium plan rents a carts for $\$12$ per day plus a one time fee of $\$126.05$
For how many whole days would it be cheaper to rent from the economy plan then from the premium plan?

Hi Desiree,

Suppose you rent the cart for $n$ days. Under the economy plan it costs $\$26$ per day so what is the cost for $n$ days? Under the premium plan the cost is $\$126.02$ plus $\$12$ per day. Under this plan how much does it cost for $n$ days? Set these two quantities equal and solve for $n.$ For any number of days larger than the $n$ you found the premium plan will will be less expensive.

Penny

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