Question 1208367
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If Simon gave 30% of his sweets to Terry they will have the same number of sweets. 
If Simon gave 250 sweets to Terry, Terry will 80% more sweets than Simon. 
How many sweets does Simon have.
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<pre>
x = # of Simon' sweets;

y = # of Terry' sweets.


From the problem, we have two equations.

First equation is

    (1-0.3)x = y + 0.3x   (first statement),

which  simplifies to

    0.7x = y + 0.3x  --->  0.7x - 0.3x = y  --->  0.4x = y.



Second equation is

    x - 250 = = (y + 250) - 0.8*(x-250)  (second statement),

which  simplifies to

    x - 250 = y + 250  - 0.8x + 200,

    x - 250 - 250 - 200 = y - 0.8x

    x - 700 = y - 0.8x

    y = 1.8x - 700.

    

So, we have this system of two equations

    y = 0.4x             (1)

    y = 1.8x - 700       (2)


Equations  (1) and (2) have left sides identical, so their right sides are equal

    0.4x = 1.8x - 700

    700 = 1.4x 

    x = 700/1.4 = 500.


Thus Simon has 500 sweets.

From equation (1), Terry has 0.4*x = 0.4*500 = 200 sweets.


<U>ANSWER</U>.  Simon has 500 sweets.
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Solved.