Cat 1 # 24

[sneha_patel60]

A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?

11/30

29/60

17/30

19/30

11/15

in the explanation, they state that "The new tower is not itself three times the size of the old wing; the problem states that the capacity of the entire hospital is three times its original value, so the new tower has twice as many beds as the old wing. "

but i dont get why the new tower has TWICE as many beds....where does this info come from?
someone please help!! thanks :)

[jnelson0612]

Sure!

In the second half of the first sentence the problem states: "the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built".

Let's use actual numbers to show ourselves what is going on.

Let's assume that the hospital previously had 10 beds. Since the new tower was built, the hospital now has 3 times the number of beds available before the tower. That means that the enlarged hospital has 30 beds.

So we know:
old hospital--10 beds
old hospital + new tower--30 beds
new tower must be 20 beds

Thus, the new tower has twice as many beds as does the old hospital.

Hope this helps!

[niitsm]

dear instructor

By assuming 30 as total won't we get stuck as the occupied bed in the org hospital was 1/3. I have tried with 10/20/30 but was not able to get to the right answere. can you please explain what precaution we need to take while assuming the no in fraction questions. I thought as given fraction is 1/3 & 1/5 30 would be the viable option .

[jnelson0612]

dear instructor

By assuming 30 as total won't we get stuck as the occupied bed in the org hospital was 1/3. I have tried with 10/20/30 but was not able to get to the right answere. can you please explain what precaution we need to take while assuming the no in fraction questions. I thought as given fraction is 1/3 & 1/5 30 would be the viable option .

That's generally a good rule to follow. I was just making up numbers to illustrate the general principle, not showing you the correct numbers to come up with. My bad! I agree that we should use multiples of 3 and 5. Yes, so let's say that the old hospital had 30 beds and with the new addition we now have 90 beds total. Thus, the new hospital has 60 beds. Now we're set! :-)

[rkafc81]

hi

how would I go about attacking this one, and setting it up properly?

i got really messed up trying to set it up...

thanks!

[geezer0305]

hi

how would I go about attacking this one, and setting it up properly?

i got really messed up trying to set it up...

thanks!

Hi,

this questions is relatively easy as long as one understands it. I messed up too because i did not read the question properly

as long as you get this line " the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built.", i think you should be good to go....

Let,
Beds before = n1
Beds after = n2

The aforementioned statement gives us : n1+n2 = 3n1
=> n2 = 2n1

Regards,

[jlucero]

Good use of algebra, geezer0305. I'll add that I like Jamie's use of picking numbers, but when I see fractions like 1/3 and 1/5, I'm immediately thinking of LCM = 15. Start with 15 in the original tower and add geezer0305 equation New = 2 * Old = 2 * 15 = 30
Old wing has 15, New wing has 30, and I'd double check those numbers to make sure that it fits in with the problem itself.