Lesson How many coconuts are there in each of five baskets?

How many coconuts are there in each of five baskets?

Problem 1

Let  be the number of coconuts in the i-th basket, i = 1, 2, 3, 4, 5.
Then we have this system of 5 equations in 5 unknowns:

 +  = 52,    (1)
 +  = 43,    (2)
 +  = 34,    (3)
 +  = 30,    (4)
 +  = 47.    (5)

Add all 5 equations (1) to (5)  (both sides). You will get

 = 206,   or,  dividing both sides by 2

 = 103.   (6).


Now, add equations (1) and (4) and distract this sum from (6). You will get
 = 103 - 52 - 30 = 21.
So, there are 21 coconuts in basket #3.


Next, from equation (2) you can easily get get
 = 43 -  = 43 - 21 = 22.
So, there are 22 coconuts in basket #2.


Then from equation (1) you can easily get
 = 52 -  = 52 - 22 = 30.
So, there are 30 coconuts in basket #1.


Similarly, from equation (3) you can easily get
 = 34 -  = 34 - 21 = 13.
So, there are 13 coconuts in basket #4.

Then from (4) you have   = 30 -  = 30 - 13 = 17 coconuts in basket #5.

Answer.  30, 22, 21, 13 and 17 coconuts in baskets 1 to 5 respectively.