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

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by wislylictag

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by wislylictag

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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.

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.