Five times the reciprocal of a number equals the sum of 3/2 the reciprocal of the number and 7/6. What is the number
To solve this problem, let's first define the unknown number as "x".
The first part of the problem states that "Five times the reciprocal of a number equals..." which can be represented as 5 * (1/x).
The second part of the problem states "...the sum of 3/2 the reciprocal of the number and 7/6" which can be represented as (3/2)*(1/x) + (7/6).
Now we can set up the equation:
5 * (1/x) = (3/2)*(1/x) + (7/6)
To solve this equation, we'll need to find a common denominator. In this case, the least common denominator (LCD) is 6.
Multiplying both sides of the equation by 6x, we get:
30 = 9 + 7x
Next, subtracting 9 from both sides of the equation:
30 - 9 = 7x
Simplifying, we have:
21 = 7x
Finally, dividing both sides of the equation by 7:
21/7 = x
x = 3
So the number is 3.