Question 1171419
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Bob and John had $540.00 altogether. Bob gave 1/7 of his money to John. 
In return John gave 1/4 of his total amount he had to Bob. 
Then they had both an equal amount of money.
How much did Bob have at first.
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        This problem is good to solve it by the  BACKWARD  method.



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They started having $540 altogether.


The money did not get out and did not come from outside: they circulated inside.


The problem says that they finished having equal amounts.
Hence, at the end, Bob and John had $170, each.


Before it, John gave 1/4 of his total amount he had to Bob.
So, John left with 3/4 of the amount he has before it, which is $270
Hence, immediately before it, John had  {{{(4/3)*270}}} = 360 dollars,
and John gave 360/4 = 90 dollars to Bob.
Hence, when John had 360 dollars, Bob had 270-90 = 180 dollars.


Thus we completed one step back and found that before Bob gave 1/7 of his money to John,
they had $360 (John) and $180 (bob).


Now we know that after Bob gave 1/7 of his money to John, Bob left with 6/7 of his money, which is $180.
Hence, before this giving, Bob's initial money was  {{{(7/6)*180}}} = $210.


Hence, John's initial money was $540 - $210 = $330.


<U>ANSWER</U>.  Initially, Bob had $210,  John had $330.


<U>CHECK</U>.   (Bob, John)          (Bob,        John)             (Bob,        John)

         (210, 330)    --->   (210-30=180, 330+30=360)  --->  (180+90=270, 360-90=270).    ! correct !
</pre>

Solved mentally, without using equations, by the BACKWARD method.