Question

When ​one-fourth of a number is added to ​one-fifth of the​ number, the sum is 18. What is the​ number?

Answer 1

unknown number is 40

Explanation:

Let x be the unknown number

one-fourth of a number is added to ​one-fifth of the​ number

`(1)/(4)x+(1)/(5) x`

sum is 18

`(1)/(4)x+(1)/(5) x=18`

To solve for x take LCD 20

`(5)/(20)x+(4)/(20) x=18\\ (9)/(20) x=18\\`

multiply both sides by 20

`9x= 360`

divide both sides by 9

x=40

Answer 2

The number is 40.

Explanation:

Let the number be n.

When ​one-fourth of a number is added to ​one-fifth of the​ number, the sum is 18

`(n)/(4)+(n)/(5)=18\\\\(5n+4n)/(4* 5)=18\\\\9n=4* 5* 18\\\\n=20* 2\\\\n=40`

The number is 40.