Question

I think of a number. If I divide the sum of 6 and the number by 3,the result is 4 more than one quarter of the number. Find the number.

Answer 1

24

Explanation:

Let the number be x.

Sum of the number and 6:
`6+x`

Divide it by 3:
`(6+x)/(3)`

Result is 4 more than one quarter of the number:

`(6+x)/(3) =4+(1)/(4) x`

Multiply both sides by 12:

`(6+x)/(3)\cdot \:12=4\cdot \:12+(1)/(4)x\cdot \:12`

Simplify:

`4\left(x+6\right)=48+3x`

Expand:

`4x+24=48+3x`

Subtract 24 from both sides:

`4x+24-24=48+3x-24`

`4x=3x+24`

Subtract 3x from both sides:

`4x-3x=3x+24-3x`

`x=24`

The number is 24.