One number is 5 times another?

Question

I am looking for someone who can help me figure out the steps to this problem

One number is 5 times another. If the sum of their reciprocals is 1/5 find the two numbers. Define the variables you use, and remember to check your solutions.

Answer 1

Let the number is a & 5a.
One of them is 5 times the other.
And then, solve this :
1/a + 1/5a = 1/5
5/5a + 1/5a = 1/5
6/5a = 1/5
Cross-multiply them, we get :
30 = 5a
a = 6
The numbers are 6 and 30.
Let's check :
1/6 + 1/30 = 5/30 + 1/30 = 6/30 = 1/5
It's true.

So, the number is 5 & 30.

Answer 2

X = 5 times Y
1/X + 1/Y = 1/5
1/5Y + 1/Y = 1/5

Multiply both sides by 5Y
1 + 5 = Y

6 = Y

30 = X

1/30 + 1/6 = 1/30 + 5/30 + 6/30 = 1/5

Answer 3

let the smaller of the 2 numbers be x, so the other number will be 5x.

also given

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

we have

(5x+x)/(x(5x)) = 1/5
6x/5x^2 = 1/5

cross-multiplying:

30x = 5x^2
5x^2 - 30x = 0

divide by 5:

x^2 - 6x = 0
x(x-6) = 0

solve for x, x=0 or 6

if x=6, (the smaller number), then the bigger number will be 5x6=30.

The 2 numbers are 6 & 30.

Answer 4

So,
x = 5y

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

Substituting x in terms of y
(1/5y) + (1/y) = 1/5

6/5y = = 1/5

y= 6

x = 5y ==> x=30

Answer 5

so: y=5x
1/y+1/x=1/5

so substitute the first equation into the 2nd one

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

x=6
y=30

numbers are 6 and 30