You originally have x colored pencils in your pencil box. You share them equally between you and your friend. You add in 3 more colored pencils to your own box after sharing them. This gives you a total of 15 pencils.
Let's represent the number of colored pencils originally in the pencil box as "x".
After sharing them equally between you and your friend, each of you will have x/2 colored pencils.
You then add 3 more colored pencils to your own box, so you have x/2 + 3 colored pencils.
This gives you a total of 15 pencils, so we can set up the equation:
x/2 + 3 = 15
Solving for x:
x/2 = 15 - 3
x/2 = 12
Multiplying both sides of the equation by 2, we get:
x = 2 * 12
x = 24
Therefore, you originally had 24 colored pencils in your pencil box.
Let's solve this step-by-step:
1. Let's represent the number of colored pencils in the original box as "x".
2. We share the colored pencils equally between you and your friend. After sharing, you are left with "x/2" colored pencils in your own box.
3. You add 3 more colored pencils to your own box. So, the total number of colored pencils you have now is "(x/2) + 3".
4. The total number of colored pencils after adding 3 more is given as 15. So we can write the equation:
(x/2) + 3 = 15
5. Now, let's solve the equation:
Subtracting 3 from both sides: (x/2) = 12
Multiplying both sides by 2: x = 24
Therefore, you originally had 24 colored pencils in your pencil box.