Question

When a number is added to 1/5 of itself, the result is 24. The equation that models this problem is n +1/5 n = 24. What is the value n? n = 18 n = 20 n = 214/5 n = 234/5

Answer 1

Answer: Second Option

`n = 20`

Explanation:

Let's call n the number searched.

Then one fifth of this number is written as

`(1)/(5)n`

Then at 1 / 5n the number n is added.

So, we have

`n + (1)/(5)n`

Now we know that the result of this sum is equal to 24. Then we write the equation:

`n + (1)/(5)n = 24`.

Now we solve the equation:

`(6)/(5)n = 24`

Muple both sides of equality by
`(5)/(6)`

`(5)/(6) * (6)/(5)n = 24*(5)/(6)`

`n = 20`

Answer 2

For this case we must find the value of n of the following equation:

`n + \frac {1} {5} n = 24`

Taking common factor "n" from the left side of the equation we have:

`n (1+ \frac {1} {5}) = 24\\n \frac {6} {5} = 24`

Multiplying by 5 on both sides of the equation:

`6n = 120`

Dividing between 6 on both sides of the equation:

`n = 20`

Thus, the value of n is 20.

Answer:

`n = 20`