SOLUTION: kado, chado and nado are good friends in the village. one day, kado on his way to village found a basket with some apples. He took it to their playing field and divided all apples

Question 1195818: kado, chado and nado are good friends in the village. one day, kado on his way to village found a basket with some apples. He took it to their playing field and divided all apples to three equal portions. he took away his share and left. Chado came later to the same spot and saw two equal portions of apples. He mixed them and divided into elthree equal portion but there was one extra apple left. He took the extra apple along with his own share. after sometime nado arrived at the spot and took away all the apples.
When all of them met in the evening, to their suprise all of them got equal number of apples l. what is the total number of apples in the basket.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I will show two different methods for solving the problem, starting from different starting places, to demonstrate how taking a few moments to look for different ways of setting up a problem can make a big difference in how complicated the solution is.

First method....
Probably the most obvious starting point is to let the variable be what the question asks for -- the number of apples in the basket. The solution then might go like this....

(1) x = original number of apples

(2) kado divided the apples into three equal portions and took one of them. So the number of apples he took was (1/3)x, and the number remaining was (2/3)x.

(3) chado then came and saw the two piles of apples with a total of (2/3)x apples. He mixed them and divided them into three equal piles, with one apple left over.
Let y be the number of apples in each of the three piles; then, with one apple left over, the number of apples remaining, (2/3)x, is equal to the number in the three piles, plus the one extra apple:

3y+1 = (2/3)x
3y = (2/3)x-1
y = (2/9)x-1/3

He then took one pile, containing (2/9)x-1/3 apples, plus the extra apple; so the number he took was (2/9)x+2/3.
But the number he took was the same as the number kado took, so

(2/9)x+2/3 = (1/3)x
2/3 = (1/9)x
x = 9(2/3) = 6

ANSWER: The original number of apples was 6.

CHECK:
original number: x = 6
number in each pile kado made: 6/3 = 2
number kado took: (1/3)x = 2
number remaining: 6-2 = 4
number in each pile chado made: 1
number chado took (one pile plus the extra apple): 1+1 = 2
number left for nado: 4-2 = 2

That solution method worked; but it involved some ugly fractions. So let's start from a different place and see if the solution is easier.

Let x be the number of apples in each pile chado made.
Then the number of apples chado found was 3x+1.
chado took one pile (x) plus the extra apple, so he took x+1 apples.
That left (3x+1)-(x+1) = 2x apples for nado.
But chado and nado got equal numbers of apples:
x+1 = 2x
x = 1
So chado and nado each got 2 apples.
But all three of them got the same number of apples; so the original number of apples was 3*2 = 6.

ANSWER: 6

Observe that the solution by this method was far easier than by the other method....

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