Answered

IDNStudy.com, ang iyong gabay para sa maaasahan at mabilis na mga sagot. Magtanong ng anumang bagay at makatanggap ng kumpleto at eksaktong sagot mula sa aming komunidad ng mga propesyonal.

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.