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.

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Trust the above helps.

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

Cheers,

Edward