Answer:
p = 600 + 250t
t = 34
Explanation:
To find a function that describes how the cost of the lease depends on time, we need to consider the initial cost and the monthly cost of the lease. The initial cost is the down payment of $600, which is paid once at the beginning of the lease. The monthly cost is $250, which is paid every month for the duration of the lease. Therefore, the total cost of the lease after t months is:
p = 600 + 250t
This is the function that models the situation. It is a linear function with a slope of 250 and a y-intercept of 600.
To find how long can the motorcycle be leased before more than the purchase price has been paid, we need to compare the cost of the lease with the purchase price of $9100. We need to find the value of t that makes p equal to 9100. We can do this by solving the equation:
p = 600 + 250t
9100 = 600 + 250t
Subtracting 600 from both sides, we get:
8500 = 250t
Dividing both sides by 250, we get:
t = 34
This means that after 34 months, the cost of the lease will be equal to the purchase price. Therefore, to pay more than the purchase price, the motorcycle must be leased for more than 34 months.
Here's a funny way to remember this:
Why did the motorcycle renter cross the road? To get to his monthly payment!
What do you call a motorcycle that costs more than its worth? A cycle-path!
How do you make seven an even number? Just remove the "s"!