One number is 3 times another. If the sum of their reciprocals is 4, find the two numbers. __

15

this is supposed to be 4 over 15

Let the smaller number be x. The two numbers are then x and 3x. You have only one unknown now.

1/x + 1/(3x) = 4
4/(3x) = 4
1/(3x) = 1
3x = 1
x = 1/3
3x = 1

4/15 is not an answer. I don't see where you get that.

The product of two consecutives positive even numbers is 1224.What are the numbers? (Enter solutions from the smallest to largerst)

One number is three times another. The sum of their reciprocal is 4. What are the two

numbers?

Apologies for the confusion. Let's go through the steps again to find the two numbers.

Let the smaller number be x. The two numbers are then x and 3x. We have the equation:

1/x + 1/(3x) = 4

To solve this equation, we can find a common denominator:

(3 + 1) / (3x) = 4

4 / (3x) = 4

Now, let's cross-multiply:

4 * (3x) = 4 * 4

12x = 16

Divide both sides by 12:

x = 16 / 12

x = 4/3

Therefore, the smaller number is 4/3, and the larger number is 3 times that, which is 4/3 * 3 = 4.

The two numbers are 4/3 and 4.

Apologies for the oversight. Let's correct the solution.

Let's assume the smaller number is x. According to the problem, the larger number is three times the smaller number, so the larger number is 3x.

The sum of their reciprocals is given as 4, so we can write it as an equation:

1/x + 1/(3x) = 4

To solve this equation, we need to find a common denominator for the fractions. The least common multiple (LCM) of x and 3x is 3x, so we can rewrite the equation as:

(3 + 1) / (3x) = 4

Combining the fractions on the left side, we have:

4 / (3x) = 4

Now, we can cross-multiply:

4 * 3x = 4 * 4
12x = 16

Dividing both sides of the equation by 12:

x = 16 / 12
x = 4 / 3

So, the smaller number is 4/3, and the larger number is three times that:

3x = 3 * (4/3) = 4

Therefore, the two numbers are 4/3 and 4.