Question 344416: If 1/6 is added to 4 times the reciprocal of a certain number, the result is 21/10. Find the number
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x is the reciprocal of y if x*y = 1.
example:
The reciprocal of 3 is equal to 1/3 because 3 * 1/3 = 1
Let x equal the reciprocal of y.
You get 1/6 + 4*x = 21/10.
Multiply both sides of this equation by 60 to get:
10 + 240 * x = 126
Subtract 10 from both sides of this equation to get:
240*x = 116
Divide both sides of this equation by 240 to get:
x = 116 / 240
Since x is the reciprocal of y, this means that y is equal to 240 / 116
The number you are looking for should be 240 / 116.
To find out if that is true, substitute 240 / 116 for the number in your original problem statement.
The original problem statement is:
If 1/6 is added to 4 times the reciprocal of a certain number, the result is 21/10. Find the number.
If the number is 240 / 116, then the reciprocal of the number has to be 116 / 240 because 240 / 116 * 116 / 240 = 1.
So, the reciprocal we are looking for is 116 / 240.
4 * 116 / 240 = 464 / 240.
Add 1/6 to that and you get:
464 / 240 + 1/6 = 464 / 240 + 40 / 240 = 504 / 240
If this is correct, then 504 / 240 should be equal to 21 / 10
If you divide numerator and denominator of 504 / 240 by 24, then you get 21 / 10 which is the same as 21 / 10, so the answer is good.
The number you are looking for is 240 / 116.
The reciprocal of that number is 116 / 240.
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