SOLUTION: The sum of two numbers is 8 also 15 times the sum of their reciprocals is 8. Find the numbers.

Question 661631: The sum of two numbers is 8 also 15 times the sum of their reciprocals is 8. Find the numbers.
Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
x + y = 8
15(1/x+1/y) = 8
Substituting with x
15((1/8-y) + 1/y) = 8
Distributing 15
15/8-y + 15/y = 8
Multiplying both sides by 8-y
15 + 15(8-y)/y = 8(8-y)
Distributing 15 and 8
15 + 120-15y/y = 64 - 8y
15 + 120/y - 15 = 64 - 8y
Combine like terms
120/y + 8y = 64
120 + 8y^2 = 64y
120 + 8y^2 - 64y
8y^2 - 64y + 120
8(y^2 - 8y + 15)
8(y-3)(y-5)=0
y = 3 or y = 5
therefore x = 5 or x = 3
Either way, the two numbers are 3 and 5
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