WORD PROBLEMS USING SIMULTANEOUS EQUATION

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a/b is a fraction, if 2 is added to thenumerator the value of the fraction is 1/2. If 3 is added to the denominator, the fraction has a value of 1/3. The value of the sum a+b is

(a) 18 (b) 20 (c) 25 (d) 27 (e) 32

                Solution

 Step 1: a+2 = 1 ......... (1)
               b      2 
             a    = 1 ..........(2)
             b+3   3

 Cross multiply

   2(a+2) = b
  3a = b+3
2a+4=b .......... (3)
3a= b+3 ......... (4)

 Substitute b = 2a+4 in equation (4)
   
  3a= 2a+4+3
     3a= 2a+7
     3a-2a=7
        a=7

 Substitute a=7 in equation (3)

   2(7) + 4 = b
  14 + 4 = b
   18=b
So therefore a=7 and b= 18

 Step 2: find the sun of a+b
= 7 + 18 = 25
To prove that a=7 and b= 18
Substitute a=7 and b= 18 to get the actual values of the fractions

 7+2= 9  =1
 18    18  2

      7 =   7 =1
 18+3  21   3

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