If three times a number, added to 2 is divided by the number plus 5, the result is eight thirds.

Number = 34

Step-by-step explanation:

We are looking for our mystery "number". I will call this number N.

We can find out what our equation looks like based on what the question tells us.

"three times a number" is 3N

"added to 2" is + 2

Which so far is 3N + 2

"divided by the number plus 5" is ÷

Combined with the first two parts to give us (3N + 2) ÷ (N + 5)

"the result is eight third" So the above equation is equal to 8/3

Combining all these comments together to get the following equation

(3N + 2) ÷ (N + 5) = 8/3

Rearrange by multiplying both sides of the = by (N+5)

3N + 2 ÷ (N + 5) × (N + 5) = 8/3 × (N + 5)

Simplify

3N + 2 = 8/3 × (N + 5)

3N + 2 = 8N/3 + 40/3

Bring the N numbers to one side and the non N numbers to the other side, by subtracting 2 from both sides of the =

3N + 2 - 2 = 8N/3 + 40/3 - 2

Simplify

3N = 8N/3 + 34/3

and then subtracting 8N/3 from both sides

3N - 8N/3 = 8N/3 - 8N/3 + 34/3

Simplify

1N/3 = 34/3

Simplify for our final answer by multiplying both sides of the = by 3

1N/3 x 3 = 34/3 x 3

N = 34

Many of these steps can be skipped when solving for yourself but I wanted to be thorough

ok then what happened.