What's the numbers?
Number Theory
Level
1
A number added by the 2/3 of it is equal to 1 2/3 of the number. If the reciprocals of the numbers is added, the sum is 1/6. What is the product of the 2 numbers?
The answer is 150.
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1 solution
Let X be the number. If the reciprocal of the number and the reciprocal of 2/3 of it is added, it's sum is 1/6. The solution is this: (1/X + 3/2(1/X)) = 1/6, (1/X +3/2X) = 1/6, their LCD is 6X. So, 6X(1/X + 3/2X = 1/6)6X. Then 6 + 9 = X. So X is equal to 15 and the 2/3 of it is 10. 15 x 10 = 150. Hence, 150 is the answer.