# Abby Betty and Candy had 864 cards.......

"Abby Betty and Candy had 864 cards........ " is a math question in Singapore.

Since many students stumble to get answer for this question, we give step by step solution here.

## Abby Betty and Candy had 864 cards...... - Solution

Question :

Abby, Betty and Candy had 864 cards. Betty won some of the cards from Abby and as a result, Betty's cards increased by 50%. Candy then won some cards from Betty and Candy's cards increased by 40%. Finally, Candy lost some of her cards to Abby and Abby's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent more cards did Abby have than Betty at first ?

Solution :

In the end,

Each person would have  864 /3  =  288 cards

Because, in the end, they realised that they each had an equal number of cards.

Let us consider this point from the question.

"Finally, Candy lost some of her cards to Abby and Abby's cards increased by 20%"

Let "x" be the number of cards having had by Abby before 20% increment.

Then, the number of cards after 20% increment is 120% of "x".

That is 1.2x and 1.2x  =  288 ----> x  =  240

So, Abby won 48 cards (288-240) from Candy.

Before the lose to Abby, Candy would have had  cards 336 (288+48 = 336).

Candy had 336 cards after winning some cards from Betty.

That is 40% increment in Candy's cards.

If candy had "c" number of cards originally, then

140% of c  =  336

1.4c  =  336

c  =  240

So, Candy had 240 cards at first and she won 96 cards (336-240  =  96) from Betty.

Before losing some cards to Candy, Betty would have had 384 cards (288+96  =  384).

Betty had 384 cards after winning some cards from Abby.

That is 50% increment in Betty's cards.

If Betty had "b" number of cards originally, then we have

150% of b  =  384

1.5b  =  384

b  =  256

So, Betty had 256 cards at first

Number of cards having had by by Abby at first is

=  864 -  (256 + 240)

=  864 - 496

=  368

At first the number of cards were having had by

Abby  =  368

Betty  =  256

Candy  =  240

Number of cards that Abby had more than Betty is

=  368 - 256

=  112

Percentage  =  (112 / 256) x 100 %

Percentage  =  43.75 %

Therefore, Abby had 43.75 % more cards than Betty at first.

After having gone through the stuff given above, we hope that the students would have understood the solution given to the math problem.

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