Question

The sum of one-third of a number and three-fourths of the number exceeds that number by one. Which equation could be used to find the number? n = n + 1 n + n = n - 1 n + n = n + 1

Answer 1

`(n)/(3) + (3n)/(4) = n+1`

`4n + 9n = n+1`

`13n = n+1`

`13n-n = 1`

`12n = 1`

Answer 2

`(n)/(3)` +
`(3n)/(4)` = n +1.

Number = 12.

Explanation:

Given : The sum of one-third of a number and three-fourths of the number exceeds that number by one.

To find : Which equation could be used to find the number.

Solution : We have given a statement

Let a number = n

According to question

One third of a number =
`(n)/(3)`.

Three - fourths of the number =
`(3n)/(4)`.

Sum of their is exceeds that number by one.

`(n)/(3)` +
`(3n)/(4)` = n +1.

Taking common denominator

`(4n+9n)/(12)` = n+1 .

`(13n)/(12)` = n+1.

On subtracting n both sides.

`(13n)/(12)` -n = 1

Taking common denominator

`(13n -12n)/(12)` = 1

`(n)/(12)` = 1

On multiplying by 12 both sides

n= 12.

Therefore,
`(n)/(3)` +
`(3n)/(4)` = n +1.

Number = 12.