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Chapter 3: Problem 12

Luciano measured the amount of water that evaporated over a period of time from a container holding \(w\) ounces of water, where \(w\) is greater than 12. By the end of the first day, the cup had lost 2 ounces of water. By the end of the 7th day, the cup had lost an additional 8 ounces of water. By the end of the 11th day, the cup had lost half of the water that remained after the 7th day. Which of the following represents the remaining amount of water, in ounces, in Luciano's container at the end of the 11th day? A) \(\frac{w-2}{8}\) B) \(\frac{w-2}{2}-10\) C) \(\frac{1}{2} w-10\) D) \(\frac{w-10}{2}\)

Short Answer

Expert verified
\(\frac{1}{2}w - 5\)

Step by step solution

01

Determine the amount of water after 1st day

To find the amount of water after the 1st day, subtract 2 ounces from w (the initial amount of water): \(w-2\)
02

Determine the amount of water after 7th day

By the end of the 7th day, the container loses an additional 8 ounces of water. So, subtract 8 ounces from the amount of water after the 1st day: \(w-2-8\) Simplify it: \(w-10\)
03

Determine the amount of water evaporated after 11th day

By the end of the 11th day, the container loses half of the water remaining after the 7th day. So, we need to find half of the amount after the 7th day: \(\frac{1}{2}(w-10)\)
04

Determine the remaining amount of water after 11th day

Now, we need to subtract the amount of water evaporated after the 11th day from the amount of water after the 7th day: \((w-10) - \frac{1}{2}(w-10)\)
05

Simplify the expression

To simplify the expression, we can distribute the negative sign on the right side and then combine like terms: \(w-10 - \frac{1}{2}w + \frac{1}{2}10\) Now, combine like terms: \(\frac{1}{2}w - 10+5\) Simplify: \(\frac{1}{2}w - 5\) So, the remaining amount of water in Luciano's container at the end of the 11th day is: \(\boxed{\frac{1}{2}w - 5}\) However, none of the given options match with the above result. Check the exercise to make sure it is well posed and has a unique solution.

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