Given the following equations:
5(a+b) = 3125, and
3125(a-b) = 5,
what is the value of b?


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Answer:

 

12
5
 

Step by Step Explanation:
  1. We know that 3125 = 55. If we replace 3125 by 5 to the power 5, we get:
    55(a-b) = 5
    5(a+b) = 55
  2. From the above step we have:
    5(a - b) = 1
    or, 5a - 5b = 1 ------(1)

    a + b = 5 ------(2)
    or, 5a + 5b = 25 ------(3)   [On multiplying by 5.]
  3. Adding equation (1) and (3) we have:
    10a = 26
    Or, a =  
    13
    5
     
  4. Putting this value in equation (2) we get:
    b = 5 - a
    Or, b = 5 -  
    13
    5
     
    Or, b =  
    12
    5
     

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