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.
a) Write an equation and show all of your steps for solving x (the original number of pencils in your box)
b) What if you wanted to have at least 20 pencils left in your box? How many pencils would you have needed originally?
c) Write an inequality and show all steps for solving for x.
a) Let's set up an equation to solve for x.
First, you share equally between you and your friend, which means you each get x/2 colored pencils.
Then, you add 3 more colored pencils to your own box, making the total number of pencils in your box (after sharing) x/2 + 3.
Finally, we know that the total number of pencils you have now after adding 3 more is 15. Therefore, the equation becomes:
x/2 + 3 = 15
To solve for x, we can start by subtracting 3 from both sides:
x/2 = 15 - 3
x/2 = 12
Next, we can multiply both sides by 2 to get rid of the fraction:
2 * (x/2) = 2 * 12
x = 24
So, the original number of colored pencils in your box was 24.
b) If you wanted to have at least 20 pencils left in your box, we can modify the equation from part (a).
After sharing equally with your friend, you each get x/2 colored pencils. If you want to have at least 20 pencils left in your box, you would have x/2 - 3 pencils left after sharing.
The modified equation becomes:
x/2 - 3 ≥ 20
To solve for x, we can start by adding 3 to both sides:
x/2 - 3 + 3 ≥ 20 + 3
x/2 ≥ 23
Next, we can multiply both sides by 2:
2 * (x/2) ≥ 23 * 2
x ≥ 46
Therefore, you would have needed originally at least 46 pencils in your box.
c) The inequality for this scenario would be:
x/2 + 3 ≥ 20
To solve for x, we can start by subtracting 3 from both sides:
x/2 ≥ 20 - 3
x/2 ≥ 17
Next, we can multiply both sides by 2:
2 * (x/2) ≥ 17 * 2
x ≥ 34
So the inequality solution is x ≥ 34, indicating that the original number of pencils in your box should be at least 34.
make a shorter awnswer
a) Let's solve for x (the original number of pencils in your box):
Step 1: Initially, you have x colored pencils in your box.
Step 2: You share them equally with your friend, so you have x/2 colored pencils left in your own box.
Step 3: You add 3 more colored pencils to your own box, which gives you a total of x/2 + 3 colored pencils.
Step 4: The total number of colored pencils after adding 3 more is 15.
So, we can write the equation: x/2 + 3 = 15.
To solve for x, we can subtract 3 from both sides of the equation:
x/2 + 3 - 3 = 15 - 3,
x/2 = 12.
To isolate x, we can multiply both sides of the equation by 2:
2(x/2) = 12(2),
x = 24.
Therefore, the original number of colored pencils in your box was 24.
b) If you want to have at least 20 pencils left in your box, we can modify the equation:
Step 1: Initially, you have x colored pencils in your box.
Step 2: You share them equally with your friend, so you have x/2 colored pencils left in your own box.
Step 3: You add 3 more colored pencils to your own box, which gives you a total of x/2 + 3 colored pencils.
Step 4: The total number of colored pencils you want to have left in your box is 20.
So, we can write the equation: x/2 + 3 = 20.
To solve for x, we can subtract 3 from both sides of the equation:
x/2 + 3 - 3 = 20 - 3,
x/2 = 17.
To isolate x, we can multiply both sides of the equation by 2:
2(x/2) = 17(2),
x = 34.
Therefore, you would have needed originally at least 34 colored pencils in your box to have at least 20 left after sharing and adding 3 more.
c) The inequality for this problem is:
x/2 + 3 ≥ 20.
To solve for x, we can subtract 3 from both sides of the inequality:
x/2 + 3 - 3 ≥ 20 - 3,
x/2 ≥ 17.
To isolate x, we can multiply both sides of the inequality by 2:
2(x/2) ≥ 17(2),
x ≥ 34.
Therefore, the original number of colored pencils in your box must be greater than or equal to 34 in order to have at least 20 pencils left.
a) Let's break down the information provided in the question.
You initially have x colored pencils in your pencil box. You share them equally with your friend, so each of you gets x/2 colored pencils.
After sharing, you add 3 more colored pencils to your box, giving you a total of x/2 + 3 colored pencils.
According to the question, this total is 15 pencils.
So, we can write the equation as:
x/2 + 3 = 15
To solve for x, we need to isolate the variable x. Let's go through the steps:
Step 1: Subtract 3 from both sides of the equation:
x/2 + 3 - 3 = 15 - 3
x/2 = 12
Step 2: Multiply both sides of the equation by 2 to eliminate the fraction:
2(x/2) = 2 * 12
x = 24
Therefore, the original number of pencils in your box is 24.
b) To find out how many pencils you would need to have originally if you want to have at least 20 pencils left in your box, we can set up the following inequality:
x/2 + 3 >= 20
To solve for x, we need to isolate the variable x. Let's go through the steps:
Step 1: Subtract 3 from both sides of the inequality:
x/2 + 3 - 3 >= 20 - 3
x/2 >= 17
Step 2: Multiply both sides of the inequality by 2 to eliminate the fraction:
2(x/2) >= 2 * 17
x >= 34
Therefore, you would need to have at least 34 pencils originally to have at least 20 pencils left in your box.
c) The inequality for this part is already set up in part b:
x/2 + 3 >= 20
You can solve this inequality by following the steps explained in part b, which gives you the solution x >= 34.