Question: The Crandalls' hot tub is half filled.

[sophiaefrem]

Hi, I tried to find the ManhattanGMAT Strategy Guide forum but, for some reason, could not.

I am having an issue with a question in the FDP Strategy Guide, pages 94-95.

Question:

The Crandalls' hot tub is half filled. Their swimming pool, which has a capacity four times that of the tub, is filled to four fifths of its capacity. If the hot tub is drained into the swimming pool, to what fraction of its capacity will the pool be filled?

Answer, as given by MGMAT:

The denominators in this problem are 2 and 5. The Smart Number is the least common denominator, which is 10. Therefore, assign the hot tub a capacity of 10 units. SInce the swimming pool has a capacity 4 times that of the pool, the swimming pool has a capacity of 40 units. You know that the hot tub is only half filled; therefore, it has 5 units of water in it. The swimming pool is four-fifths of the way filled, so it has 32 units of water in it. Add the 5 units of water from the hot tub to the 32 units of water that are already in the pool: 32+5=37. With 37 units of water and a total capacity of 40, the pool will be filled to 37/40 of its total capacity.

My question is: Why do we use two different denominators, 10 and 40, instead of both having the same LCM. We are adding fractions, no?

[magauovazamat]

Hi, I tried to find the ManhattanGMAT Strategy Guide forum but, for some reason, could not.

I am having an issue with a question in the FDP Strategy Guide, pages 94-95.

Question:

The Crandalls' hot tub is half filled. Their swimming pool, which has a capacity four times that of the tub, is filled to four fifths of its capacity. If the hot tub is drained into the swimming pool, to what fraction of its capacity will the pool be filled?

Answer, as given by MGMAT:

The denominators in this problem are 2 and 5. The Smart Number is the least common denominator, which is 10. Therefore, assign the hot tub a capacity of 10 units. SInce the swimming pool has a capacity 4 times that of the pool, the swimming pool has a capacity of 40 units. You know that the hot tub is only half filled; therefore, it has 5 units of water in it. The swimming pool is four-fifths of the way filled, so it has 32 units of water in it. Add the 5 units of water from the hot tub to the 32 units of water that are already in the pool: 32+5=37. With 37 units of water and a total capacity of 40, the pool will be filled to 37/40 of its total capacity.

My question is: Why do we use two different denominators, 10 and 40, instead of both having the same LCM. We are adding fractions, no?

Hello my friend!

I am a student as you are and I can help you in this question.

In this question you have two denominator because the problem wording tells an answer: Their swimming pool, which has a capacity four times that of the tub, is filled to four fifths of its capacity. means "Swimming pool" has a capacity 4 times that of the "Tub" or Swimming pool=4*Tub. This means you have to multiply LCM of 10, which is Tub's capacity, to 4 (10*4=40), which is "Swimming pool's capacity".

Think this helps!!!

[jlucero]

Well explained, magauovazamat.