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 By: Rohana (offline)  Sunday, March 17 2013 @ 04:42 AM CDT (Read 1141 times)
Rohana

Hi! I am stucked with these two challenging problems. Pls help.

1. In the classroom, when a boy stands up, the number of boys sitting becomes 4/5 of the number of girls sitting. On the other hand, when a girl stands up, the number of girls sitting becomes 8/7 of the number of boys sitting. How many boys and girls are there in the class?

2. Ellen, Fiona and Gina had a total of 320 Marlbe's. Ellen had the least number of marbles. The ratio of Fiona's marbles to Gina's marbles was 5:4 at first. After Ellen and Fiona had each lost 1/2 of their marbles, Fiona had 50 marbles more than Ellen. Given that the three girls had 220 marbles left, how many marbles did Ellen have at first?

Junior

Registered: 01/24/12
Posts: 18

 By: echeewh (offline)  Sunday, March 17 2013 @ 09:00 PM CDT
echeewh

hey Rohana,

Following pls find my worked solutions:

Q1

<1 B stands up>

<seated>
B : G
4 : 5

<1 G stands up>

<seated>
B : G
7 : 8

In both cases, the number of B and G seated remains the same. Applying <unchanged total> concept for these two ratios, we have ...

B : G Total
4 : 5 9 -- (1)

B : G Total
7 : 8 15 -- (2)

Lowest common multiple is 45. Hence, Multiply (1) 5x, and (2) 3x. We have ...

B : G Total
20 : 25 45 -- (3)

B : G Total
21 : 24 45 -- (4)

Hence, number of B and G in class = 45 + 1 = 46

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

Q2

F |-----|-----|-----|-----|-----|
G |-----|-----|-----|-----|
E |-------|

Total: 320

<process>
E, F each lost 1/2 of their marbles.
Split the 5 parts of F into 10 equal units(u) (i.e.each part of F = 2u ).
Likewise, the 4 parts that G had = 8u.
Of these 10u that F had, 5u were lost.
Lost = 5u of F + (1/2)p of E = 100 {320 - 220}
Hence, the <after> model ...

<After>

F |--|--|--|--|--|
G |--|--|--|--|--|--|--|--|
E |---|

Total: 220

<after>:
5u of F and (1/2)p of E = 100 {same as Lost qty}
So, 8u (G) --> 220 - 100 = 120
1u --> 15

F + G (after) = 13u --> 13 × 15 = 195
Hence, E (after) = 220 - 195 = 25

E (at first) = 25 × 2 = 50

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

Trust the above helps.

Do let me know again if these are different from your Answerkey or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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