One number is 4 times another number. The sum of their reciprocals is 1/4. What are the numbers?
Let's call the smaller number "x". According to the problem, the larger number is 4 times x, or 4x.
We know that the sum of their reciprocals is 1/4. That means:
1/x + 1/4x = 1/4
To solve for x, we can start by multiplying both sides of the equation by the least common denominator, which is 4x:
4 + 1 = x
5 = x
So the smaller number (x) is 5. And the larger number (4x) is:
4(5) = 20
Therefore, the two numbers are 5 and 20.