Answer:
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
<em>"</em>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