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 By: JessicaTan (offline)  Saturday, April 13 2013 @ 01:23 AM CDT (Read 755 times)
JessicaTan

Please help with working solution. (Answer key : (a) 588, (b) 20%)

The total number of cards in Box A, Box B and Box C was 1022 at first. Denise gave away 3/5 of the cards from Box A, put 70 more new cards into Box B and added some cards into Box C until the number of cards in Box C became thrice its original number. The ratio of the number of cards in Box A to that in Box B to that in Box C then became 2 : 5 : 9.

(a) How many more cards were there in Box C than Box A in the end?
(b) What was the percentage increase in the number of cards in Box B ?

Thanks

Regular Member

Registered: 10/17/09
Posts: 82

 By: echeewh (offline)  Saturday, April 13 2013 @ 08:19 AM CDT
echeewh

Hi Jessica,

Following pls find my worked solution:

*** - alignment purpose

Apply <work backwards> method, we have ...

<After>
A : B : C
2 : 5 : 9

<process>
C: 3x original number
B: +70
A: (3/5) given away

<Before>
C: 3u *** {9u ÷ 3}
B: 5u - 70
A: 5u *** {since (2/5) = 2u}

Given that total number of cards in Box A, Box B and Box C was 1022 at first, we have ...

13u --> 1022 + 70 = 1092
1u --> 84

(a)
C - A (end) = 9u - 2u = 7u
7u --> 7 × 84 = 588

(b)
% increase in number of cards in box B:

Number of cards in B (before) = 5u - 70
5u - 70 --> (5 × 84) - 70 = 420 - 70 = 350

(70 / 350) × 100 = 20%

========

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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