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By: achieve_goal (offline)  Sunday, July 22 2012 @ 04:12 AM CDT (Read 836 times)  
achieve_goal

1. The ratio of Ahmad's cards to Benny's cards was 3:4. After Ahmad bought another 9 cards and Benny

lost 18 cards, the ratio became 3:2. Find the total number of cards Ahmad and Benny had at first.

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By: echeewh (offline)  Sunday, July 22 2012 @ 08:23 AM CDT  
echeewh

Hey there,

Following pls find my worked solution:

<Before>
A : B
3 : 4

<process>
A: +9; B: -18

<After>
A : B
3 : 2

Using Simultaneous method (aka Parts n Units), we use Parts (p) for <Before> ratio and Units (u) for <After> ratio as follows:

3p + 9 --> 3u
4p - 18 --> 2u

Re-arranging the above equations, we have ...

3u - 3p --> 9 --- (1)
4p - 2u --> 18 --- (2)

Since question is to find total number of cards at first, we will eliminate (u) as shown:

(1)x2:
6u - 6p --> 18 --- (3)
(2)x3:
12p - 6u --> 54 --- (4)

(3)+(4):
12p - 6p --> 18 + 54
6p --> 72
1p --> 12

Total cards at first = 7p --> 7 x 12 = 84

Other methods used to solve this kind of problem are Model and Cross-Multiply.

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

Trust the above helps.

Do let me know again if this does not match your Answerkey or if you have further clarifications.

Cheers,
Edward

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