Question 1036738
.
Five baskets contain coconuts. the first and second baskets together have a total of 52 coconuts. 
The second and third baskets have 43 coconuts. The third and fourth baskets have 34 coconuts. 
The fourth and fifth baskets have 30 coconuts, and the first and fifth baskets have 47 coconuts. 
How many coconuts are in each basket?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let {{{x[i]}}} 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:

{{{x[1]}}} + {{{x[2]}}} = 52,    (1)
{{{x[2]}}} + {{{x[3]}}} = 43,    (2)
{{{x[3]}}} + {{{x[4]}}} = 34,    (3)
{{{x[4]}}} + {{{x[5]}}} = 30,    (4)
{{{x[1]}}} + {{{x[5]}}} = 47.    (5)

Add all 5 equations (1) to (5)  (both sides). You will get
{{{2*(x[1] + x[2] + x[3] + x[4] + x[5])}}} = 206,   or,  dividing both sides by 2
{{{x[1] + x[2] + x[3] + x[4] + x[5]}}} = 103.   (6).


Now, add equations (2) and (4) and distract this sum from (6). You will get
{{{x[1]}}} = 103 - 43 - 30 = 30.
So, there are 30 coconuts in basket #1.


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


Next, add equations (1) and (3) and distract this sum from (6). You will get
{{{x[5]}}} = 103 - 52 - 34 = 17.
So, there are 30 coconuts in basket #5.


Now, from (1) you have  {{{x[2]}}} = 52 - {{{x[1]}}} = 52 - 30 = 22 coconuts in basket #2.

And finally, from (4) you have  {{{x[4]}}} = 30 - {{{x[5]}}} = 30 - 17 = 13 coconuts in basket #4.

<U>Answer</U>.  30, 22, 21, 13 and 17 coconuts in baskets 1 to 5 respectively.
</pre>