One number is 2 times another. If the sum of their reciprocals is?

Question

1/6, what are the two numbers? I do not understand this question, help...

Answer 1

Let one number be x
The second number will be 2x

1/x + 1/(2x) = 1/6
2/(2x) + 1/(2x) = 1/6
3/(2x) = 1/6
Cross-multiply
2x = 18
x = 9

The numbers are 9 and 18

Answer 2

Change the words into numbers and variables. The numbers are x and 2x. If 1/6 is the sum of their reciprocals, then

1/6 = 1/x + 1/(2x)

The lowest common denominator is 6x, and when you convert all the fractions, you get

x/(6x) = 6/(6x) + 3/(6x)

Multiply through by 6x to get

x = 6 + 3

Thus x= 9 and the two numbers are 9 and 18.

Answer 3

Lets call the numbers x and y.

One number is 2 times the other. So lets say x = 2y.

The sum of their reciprocals is 1/x + 1/y
So that means 1/x + 1/y = 1/6

To solve the whole system, replace x with 2y to get this:
1/2y + 1/y = 1/6

Then do a bit of rearranging to find what y is. You can then x very easily (from x=2y).

Answer 4

Set it up as an algebra equation with x and 2x

1/x+1/2x=1/6
multiply both sides by 6 and x
6x/x+6x/2x=6x/6
6+3=x
x=9

Check:
1/9+1/18=2/18+1/18=3/18=1/6

Answer 5

let x be one number. Then 2x is the other number.
1/x+1/2x=1/6
2/2x+1/2x=1/6
3/2x=1/6
2x=18 (cross multiply)
x=9
so the other number is 2(9)=18
9 and 18 are the numbers.
check: 1/9+1/18=3/18=1/6

Answer 6

Let the numbers be x and 2x
According to the problem,
1/x +1/2x =1/6
or,2/2x+1/2x=1/6
or,3/2x=1/6
or2x=18 [by cross-multiplication]
or x=9
therefore the numbers are 9 and 18

Answer 7

Set it up as a system of equations. Let x be the larger number and y be the smaller one.

So, x = 2y AND
1/x + 1/y = 1/6

Substitute 2y for the x and get:
1/(2y) + 1/y = 1/6
Get a common denominator.
1/(2y)+ 1/y * 2/2 = 1/6
1/(2y) + 2/(2y) = 1/6
Add.
3/(2y) = 1/6
Cross multiply.
2y = 18
y = 9, therefore x = 18.

Test it with your original equations. It works.

Answer 8

a = 2b
(1/a) + (1/b) = 1/6

(1/2b) + (1/b) = 1/6
3/2b = 1/6
2b = 18
b = 9

a = 2b = 2*9 = 18