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Problem
Solving Many
practical problems can be transformed into equations using variables. To solve a
word problem, we need to derive a pair of simultaneous equations in terms of
these two variable to find the solution. 
Example 1:
$80
is divided between two men such that one-quarter of one person's share is equal
to 1/6 of the other. How much will each man receive? 
Let each man receives $x and $y respectively.
x + y = 80 --------(1)
1/4 x = 1/6 y
6x = 4y
3x =2y
x = 2/3 y--------(2)
Subst. (2) into (1): 2/3 y + y = 80
2y + 3y = 240
5y = 240
y = 48
Subst. y = 48 into (2): x = 2/3(48)
= 32
One man receives $32 while the other receives $48.
Example 2:
If the numerator and denominator of a fraction are each
increased by 3, the fraction is equivalent to 2/3. If the numerator and
denominator are each increased by 11, the fraction is equivalent to 4/5. Find
the fraction.
Let the numerator be x and denominator be y.
From (1): 3x + 9 = 2y +6
3x - 2y = -3 --------(3)
From (2): 5x + 55 = 4y + 44
5x - 4y = -11--------(4)
(3) x 2 6x - 4y = -6
(5) - (4) x = 5
subst. x = 5 into (3)
3(5) - 2y = -3
2y = 18
y = 9
The fraction is  . | 
