A wrod problem that I can not figure out?

Question

One number is 5 times another. If the sum of their peciprocals is 1/5, find the two numbers.

I dont even know how to begin this can I get some help

Answer 1

Let x be one of the numbers and y be the other number.

"One number is 5 times the other"

y = 5x

"The sum of their reciprocals is 1/5"

(1/x) + (1/y) = (1/5)

"Find the two numbers"

Substitute the first equation into the second to get:
(1/x) + (1/5x) = (1/5)
The common denominator on the left hand side is 5x:
(5/5x) + (1/5x) = (1/5)
Combine the two fractions:
6/5x = 1/5
Cross-multiply:
5x = 30
Solve for x:
x = 6
Then Solve for y:
y = 5x = 5(6) = 30

So your two numbers are 6 and 30.

Answer 2

are you sure it's peciprocals not reciprocals?
but if it is reciprocals, then:
ok well... to get a number (fraction's) reciprocal, you flip it so 3/5 becomes 5/3. Right. Now anything over 1 e.g. 12/1 = 12 and like 34/1 = 34 and so on. So then you find a number say 3. Then find what is 5 times that. So 3*5=15. 3=3/1 and 15=15/1. So the reciprocals will be 1/3 and 1/15. Now you go 1/3+1/15 which equals 2/5. Then keep on trying. I have the answer but you only asked for help.

Answer 3

let one no be x so the other no. is 5x. sum of their reciprocal is 1/x + 1/5x. This is equal to 6/5x. this is equal to 1/5. Therefore 5 and 5 in the denominator get cancelled on both the sides. so now we have 6/x=1. No multiplying both the sides of the above equation by x we get 6 = x. So the number is 6 and the other number is 5 times 6 i.e. 30.

Answer 4

Create an equation from each part.

One number, call it x, is five times another, call it y.

So X=5y

The sum of their reciprocals is 1/5. A reciprocal of a number, x, is the number which when multiplied by x is 1. So the reciprocals of these numbers, we called them x and y, are 1/x and 1/y.

1/x + 1/y = 1/5

So you have two equations:

x = 5y

1/x + 1/y = 1/5

Solve either equation for x in terms of y, substitute that value for x in the other equation to solve for y, then replace y in the first equation with its value to solve for x.

Answer 5

Let the numbers be x and 5x.

1/x + 1/(5x) = 1/5
5 + 1 = x
6 = x
5x = 30

The numbers are 6 and 30.

Answer 6

5x=1/x+1/5, solve for x ,done.