Question 1112120
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<pre>
Let M be the amount of money each person had initially.

Let A = amount Betty gave to Alan

Let C = amount Betty gave to Cathy.


Then Betty has  (M-A-C).
     Alan  has  (M+A).
     Cathy has  (M+C).


And the condition says


M - A - C = M + A - 5     (1)    ( . . . so that Alan has $5 more than Betty)
M + C     = M + A - 1     (2)    ( . . . Cathy has $1 more than Alan)


Simplify by canceling M:


-A -C = A - 5             (1')
C     = A - 1             (2')


Write in the standard form

2A + C = 5                (1'')
 A - C = 1                (2'')


Now add eq(1'')  and eq(2'').  You will get

3A = 6  ====>  A = 2.


Then from equation (2'')  C = A - 1 = 1.


<U>Answer</U>.   A = 2, C = 1.  In other words,  B gives 2 to A and B gives 1 to C.


<U>Check</U>.    Do the check on your own.
</pre>


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<U>Comment from student</U>: &nbsp;&nbsp;Thank you for &nbsp;#1112120
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<U>My response</U>:  &nbsp;&nbsp;I want to commend you for two things:


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a) &nbsp;for sending your "Thanks",  &nbsp;&nbsp;and


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b) &nbsp;for referring to the problem ID number.



Most of other users/"students" are so badly educated people that allow themselves do neither &nbsp;a) &nbsp;nor &nbsp;b).