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 By: akachan04 (offline)  Saturday, October 10 2015 @ 12:03 AM CDT (Read 720 times)
akachan04

Hi

In a museum tour, the ratio of the number of adults to the number of children was 1: 4. The ratio of the number of boys to the number of girls was 3 : 5. There were thrice as many women as men.

a) Find the ratio of the number of men to the number of boys in the museum tour.
b) Halfway through the tour, 132 girls left the museum. As result, the number of girls remaining in the tour was twice the number of women. How many children were there at the end of the tour?

Newbie

Registered: 03/03/10
Posts: 8

 By: echeewh (offline)  Saturday, October 10 2015 @ 01:00 PM CDT
echeewh

Hey <akachan04>

Following is my worked solution:

Apply <Restate the Problem> method,

A : C
1 : 4 -- (1)

M : W
1 : 3 -- (2)

B : G
3 : 5 -- (3)

Compare (1), (2):

1 part of (A) --> 4 units of (M + W)

So multiply (1)x4:

A : C
4 : 16 -- (4)

Compare (4), (3):

16 parts of (C) --> 8 units of (B + G)

So multiply (3)x2:

B : G
6 : 10 -- (5)

(a)
M : B
1 : 6

(b)
<Before>
G : W
10 : 3 -- (6)

<After>
G : W
2 : 1 -- (7)

Given that 132 girls left the museum, apply <Unchanged Qty> method since none of the Women (W) left, we have ...

(7)x3:

<After>
G : W
6 : 3 -- (8)

Compare (6), (8) and look at G <before> and <after>, we have ...

4u --> 132
1u --> 33

Total number of children (B + G) <before> = 16u { see (5) }

Since number of girls left museum is 4u, we have ...

Total number of children (B + G) <after> = 16u - 4u = 12u

12u --> 12 × 33 = 396

======

Trust this helps.

Do let me know again if there is further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 623

 By: akachan04 (offline)  Monday, October 12 2015 @ 06:12 PM CDT
akachan04

Hi Edward,

Thank you!
I have posted another 2 NYPS questions. Hope you can help to clear my doubts.

Newbie

Registered: 03/03/10
Posts: 8

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