One number is twice another. The sum of their reciprocals is 3/10. Find the number.
To solve this problem, let's assume the smaller number is "x".
According to the problem, one number is twice another, so the larger number would be 2x.
The reciprocal of a number "a" is 1/a. So, the reciprocal of the smaller number x is 1/x, and the reciprocal of the larger number 2x is 1/(2x).
The problem states that the sum of their reciprocals is 3/10. So, we can set up the equation:
1/x + 1/(2x) = 3/10
Now, let's solve the equation step by step:
First, we need to find a common denominator for the fractions on the left side of the equation. The least common denominator (LCD) is 2x, so we will multiply both fractions by 2x:
(2x/x) + (2x/(2x)) = 3/10
2 + 1 = 3/10
Simplifying the equation further, we have:
3 = 3/10
Since the left side of the equation is an integer (3) and the right side is a fraction (3/10), there is no solution to the equation. This means that the problem is inconsistent or there is an error in the given information.
Please check the problem statement and double-check whether all the details are accurately written.
Solve 1/x + 1/(2x) = 3/10
Solve for x
3/(2x) = 3/10
The two numbers are x and 2x. They ask for the larger one.