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26 Apr 2026, 13:56
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A ski rental shop charges \(x\) dollars for the first hour of a snowboard rental and \(y\) dollars for each additional hour or fraction of an hour beyond the first hour. If Marta rented a snowboard for 11.2 hours, how much did it cost in total?
(1) The cost of each additional hour is 20 percent of the cost of the first hour.
(2) The cost of a 4.5 hour rental is 150 percent of the cost of a 1.5 hour rental.
(1) The cost of each additional hour is 20 percent of the cost of the first hour.
(2) The cost of a 4.5 hour rental is 150 percent of the cost of a 1.5 hour rental.
26 Apr 2026, 13:56
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Official Solution:
A ski rental shop charges \(x\) dollars for the first hour of a snowboard rental and \(y\) dollars for each additional hour or fraction of an hour beyond the first hour. If Marta rented a snowboard for 11.2 hours, how much did it cost in total?
Total cost for 11.2 hours = \(x + 11 * y\).
That is \(x\) dollars for the first hour, then \(y\) dollars for each additional hour or fraction of an hour beyond the first. After the first hour, 10.2 hours remain, which is 10 full hours plus a fraction, so it is charged as 11 additional hours.
(1) The cost of each additional hour is 20 percent of the cost of the first hour.
This implies \(y = 0.2x\). Thus, the total cost = \(x + 11 * 0.2x = 3.2x\). But \(x\) is unknown, so the total cost is not determined. Not sufficient.
(2) The cost of a 4.5 hour rental is 150 percent of the cost of a 1.5 hour rental.
A 4.5 hour rental means 1 first hour plus 3.5 hours beyond that, which gets billed as 4 additional hours. So cost = \(x + 4y\).
A 1.5 hour rental means 1 first hour plus 0.5 hour beyond that, which gets billed as 1 additional hour. So cost = \(x + y\).
So, this statement implies \(x + 4y = 1.5(x + y)\), which simplifies to \(x = 5y\). Thus, the total cost = \(5y + 11 * y = 16y\). But \(y\) is unknown, so the total cost is not determined. Not sufficient.
(1)+(2) From (1), \(y = 0.2x\), which is equivalent to \(x = 5y\). Statement (2) gives \(x = 5y\) as well. Thus, when combining the statements, we do not have any additional info. Not sufficient.
Answer: E
A ski rental shop charges \(x\) dollars for the first hour of a snowboard rental and \(y\) dollars for each additional hour or fraction of an hour beyond the first hour. If Marta rented a snowboard for 11.2 hours, how much did it cost in total?
Total cost for 11.2 hours = \(x + 11 * y\).
That is \(x\) dollars for the first hour, then \(y\) dollars for each additional hour or fraction of an hour beyond the first. After the first hour, 10.2 hours remain, which is 10 full hours plus a fraction, so it is charged as 11 additional hours.
(1) The cost of each additional hour is 20 percent of the cost of the first hour.
This implies \(y = 0.2x\). Thus, the total cost = \(x + 11 * 0.2x = 3.2x\). But \(x\) is unknown, so the total cost is not determined. Not sufficient.
(2) The cost of a 4.5 hour rental is 150 percent of the cost of a 1.5 hour rental.
A 4.5 hour rental means 1 first hour plus 3.5 hours beyond that, which gets billed as 4 additional hours. So cost = \(x + 4y\).
A 1.5 hour rental means 1 first hour plus 0.5 hour beyond that, which gets billed as 1 additional hour. So cost = \(x + y\).
So, this statement implies \(x + 4y = 1.5(x + y)\), which simplifies to \(x = 5y\). Thus, the total cost = \(5y + 11 * y = 16y\). But \(y\) is unknown, so the total cost is not determined. Not sufficient.
(1)+(2) From (1), \(y = 0.2x\), which is equivalent to \(x = 5y\). Statement (2) gives \(x = 5y\) as well. Thus, when combining the statements, we do not have any additional info. Not sufficient.
Answer: E
