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 By: Tping (offline)  Sunday, August 12 2012 @ 05:43 AM CDT (Read 874 times)
Tping

Hi, pls help following questions, thank you.

1)
Gopal wanted to walk to a park which was 2 2/5km away from his home.
He took a short break after he had covered 1/5 of the distance.
After the break, he walked another 3/25 km.
Find the distancce that Gopal had covered.

2)
After 3/4 of the guests in Hotel Hollywood and
3/5 of the guests in Hotel Broadway checked out,
How many guests did Hotel Hollywood have at first?

Junior

Registered: 01/26/12
Posts: 25

 By: echeewh (offline)  Tuesday, August 14 2012 @ 09:02 PM CDT
echeewh

Hey Tping,

Following pls find my worked solutions:

Q1.

(1/5) x (12/5) = (12/25) km
(12/25) + (3/25) = (15/25) km = (3/5) km

==============================

Q2.

*** - buffer space for alignment purpose

<after>

B |-----|<--260-->| --> (1p + 260)
H |-----| ********** --> (1p)

<process>
3/4 of the guests in H and 3/5 of the guests in B checked out.
1/4 of guests in H, 2/5 of guests in B remained.
As (2/5) guests in B remained behind, split this (1p) into 2 equal units (u) and (260) into 130 each. Likewise, the (1p) in H is divided into (2u). So the (1p + 260) in B becomes 2 x (1u + 130), while the (1p) in H becomes (2u).
At start <before>, there should be 5 x (1u + 130) in B, while there should be 4 x (2u) in H.
Hence the <Before> model becomes as shown ..

<before>

B |--|--|--|--|--|<------------650---------->|
H |--|--|--|--|--|--|--|--|

Given that there were 5200 guests in both H,B, we have ...

B + H --> 5200
5u + 650 + 8u --> 5200
13u --> 5200 - 650 = 4550
1u --> 350

H (at first) = 8u --> 8 x 350 = 2800

Alternative method ( Simultaneous method):

H + B = 5200 -- (1)
(2/5)B - (1/4)H = 260 -- (2)

Transforming (2) into whole numbers...
(2)x20:
8B - 5H = 5200 -- (3)

As question is interested in knowing number of guests in H at first, we shall eliminate (B ).

(1)x8:
8H + 8B = 41600 -- (4)

(4)-(3):
8H - (-5H) --> 41600 - 5200
13H --> 36400
H --> 2800

Number of guests in H at first = 2800

=======================

Trust the above helps.

Do let me know if theres any clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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