SOLUTION: The sum of two numbers is 14 and the sum of their reciprocals is 7/24. Find the numbers.

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Question 133472: The sum of two numbers is 14 and the sum of their reciprocals is 7/24. Find the numbers.
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y=14 OR X=14-Y
1/X+1/Y=7/24
1/(14-Y)+1/Y=7/24
(Y+14-Y)/Y(14-Y)=7/24
14/(14Y-Y^2)=7/24 NOW CROSS MULTIPLY
7(14Y-Y^2)=14*24
98Y-7Y^2=336
7Y^2-98X+336=0
7(X^2-14X+48)=0
7(X-6)(X-8)=0
X-6=0
X=6 ANSWER.
X-8=0
X=8 ANSWER.
PROOF
6=8=14
14=14
1/6+1/8=7/24
(8+6)/48=7/24
14/48=7/24
7/24=7/24