one number is two times another number. determine the two numbers if the sum of their reciprocals is 3/8

Answer 1

Hi! The best way to start this problem is to first translate the information we're given into an equation. Let's say one number, x, is two times another number, y, so x = 2y. We know the sum of their reciprocals is 3/8, so 1/x + 1/y = 3/8.

Here we're have 2 equations we can use to find x and y. 2 equations is all we need to find the value of 2 variables, so we can get started.

We know that x = 2y, so we can substitute 2y for x in our second equation. This gives us: 1/(2y) + 1/y = 3/8

With this new equation, we can solve for y:

1/(2y) + 1/y = 3/8

1/(2y) + 2/(2y) = 3/8

3/(2y) = 3/8 ---> Now, we can cross multiply

(2y)(3) = (3)(8)

6y = 24

y = 4

Another way of doing this is looking at 3/(2y) = 3/8. We know based on this equality that 2y=8, so y = 8/2 = 4.

Now, we can simply substitute this value of y in our first equation to find x.

x = 2y

x = 2(4)

x = 8

So our answer is that the numbers are 4 and 8. You can check the answers by substituting both values into the equations we made earlier and seeing if they give us the given result!