Question

One positive number is one-fifth of another number. the difference between the two numbers is 180 find the numbers

Answer 1

One number = 225

One-fifth number = 45

Explanation:

Let the smaller number be x.

Since another number is one fifth of another be:

`\sf (1)/(5)x`

We are given that:

Difference between the two numbers is 180

So,

`\sf x -(x)/(5)=180`

Multiply both sides by 5.

`\sf x* 5 -(x)/(5)* 5=180* 5`

Simplify:

`\sf 5x -x = 900`

`\sf 4x= 900`

Divide both sides by 4.

`\sf (4x)/(4)=(900)/(4)`

`\sf x=225`

Now,

`\sf \textsf{Another number}= (x)/(5)=(225)/(5)= 45`

Therefore, the smaller number is 45 and the larger number is 225.

Answer 2

225 and 45

Explanation:

let one number be n then the other number is
`(1)/(5)` n

their difference is 180 , that is

n -
`(1)/(5)` n = 180 multiply through by 5 to clear the fraction

5n - n = 900 , that is

4n = 900 ( divide both sides by 4 )

`(4)/(4)` n =
`(900)/(4)` , then

n = 225 and
`(1)/(5)` n = 225 ÷ 5 = 45

the numbers are 225 and 45