"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.

**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.

Apart from the stuff given above, if you want to know more about "Percentage problems", please click here

Apart from the solution to the question "Abby betty and candy had 864 cards...", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**