<PRE><B>Question 271128</B>
let a = amount of money alex has originally.
let b = amount of money bobby has originally.
let c = amount of money chris has originally.


If Alex give Bobby $4, then Alex would have half as much money as Bobby.


Equation we get is:


(a-4) = (b+4)/2


multiply both sides of these equations by 2 to get:


2a-8 = b+4


subtract 4 from both sides of this equations to get:


b = 2a-12


If Bobby gives Chris 7, then Chris would have $35 more than Bobby.


equation we get is:


(c+7) = (b-7) + 35


subtract 7 from both sides of this equation to get:


c = b-7+35-7 which becomes:


c = b + 21


If Chris gives Alex 17, then Alex would have 1 more than Chris.


Equation we get is:


a+17 = c-17 + 1


subtract 17 from both sides of this equation to get:


a = c-17+1-17 which becomes:


a = c-33


We have 3 equations to work with.


They are:


b = 2a-12 (first equation)
c = b + 21 (second equation)
a = c-33 (third equation)


substitute 2a-12 for b in the second equation to get:


c = (2a-12) + 21 which becomes:
c = 2a-12+21 which becomes:
c = 2a + 9


substitute 2a+9 for c in the third equation to get:

a = (2a+9)-33 which becomes:
a = 2a+9-33 which becomes:
a = 2a-24


subtract a from both sides of this equation and add 24 to both sides of this equation to get:


a = 24 ***********************************************************


substitute 24 for a in the first equation to get:


b = 2*24-12 which becomes:
b = 48-12 which becomes:
b = 36 ***********************************************************


substitute 36 for b in the second equation to get:


c = 36 + 21 which becomes:
c = 57 ***********************************************************


we get:
a = 24
b = 36
c = 57


Now to see if this is accurate.


Equation from the first transaction is:


(a-4) = (b+4)/2


substitute 24 for a and 36 for b to get:


24-4 = 36+4/2 which becomes:
20 = 40/2 which is true !!!!!


Equation from the second transaction is:


(c+7) = (b-7) + 35


substitute 57 for c and 36 for b to get:


57+7 = 36-7 + 35 which becomes:
64 = 29 + 35 which becomes:
64 = 64 which is true !!!!!


Equation from the third transaction is:


a+17 = c-17 + 1


substitute 24 for a and 57 for c to get:


24+17 = 57-17+1 which becomes:
41 = 41 which is true !!!!!


All equations are true so the answers must be good.


Answers are:


Alex has $24
Bobby has $36
Chris has $57









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