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The sum of the reciprocals of two numbers is 7.The larger reciprocal exceeds the smaller one by 7/3.Find the numbers.

Sagot :

Taskmastersidn
We will let
x = first number
y = second number
1/x = reciprocal of the first number which is larger
1/y = reciprocal of the second number

(1)  1/x + 1/y = 7
       1/y = 7 - 1/x

(2)  1/x = 1/y + 7/3       
       1/x = (7 - 1/x) + 7/3
       1/x = 7 + 7/3 - 1/x
       1/x + 1/x = (21+7)/3 - 1/x
       2/x = 28/3
       28x = 6
       x = 6/28
       x = 3/14

(1) 1/x + 1/y = 7
      1/(3/14) + 1/y = 7
       14/3 + 1/y = 7
       1/y = 7 - 14/3
       1/y = (21-14)/3
       1/y = 7/3
       7y = 3
       y = 3/7

Therefore the two numbers are 3/14 and 3/7.