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 colored pencils in your box).
b. If you wanted to have at least 20 colored pencils left in your box, how many colored pencils would you have needed originally?
c. Write an inequality and show all steps for solving for x.
a. Let's define the variable x as the original number of colored pencils in your box.
First, you share them equally with your friend, so each of you gets x/2 colored pencils.
After that, you add 3 more colored pencils to your own box. Therefore, the total number of colored pencils in your box is (x/2) + 3.
Since the total number of colored pencils in your box is given as 15, we can write the equation as:
(x/2) + 3 = 15
To solve for x, we can first subtract 3 from both sides of the equation:
(x/2) = 12
Next, we can multiply both sides of the equation by 2 to isolate x:
x = 2 * 12
x = 24
So, the original number of colored pencils in your box was 24.
b. To determine how many colored pencils you would have needed originally to have at least 20 left, we can set up the following inequality:
(x/2) + 3 >= 20
First, we can subtract 3 from both sides of the inequality:
(x/2) >= 17
Next, we can multiply both sides of the inequality by 2 to isolate x:
x >= 2 * 17
x >= 34
Therefore, you would have needed at least 34 colored pencils originally to have at least 20 left.
c. The inequality we set up in part b was:
(x/2) + 3 >= 20
To solve for x, we can follow these steps:
1. Subtract 3 from both sides of the inequality:
(x/2) >= 17
2. Multiply both sides of the inequality by 2 to isolate x:
x >= 34
So, the solution to the inequality is x >= 34, meaning the original number of colored pencils in your box needs to be at least 34 to have at least 20 left.
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 colored pencils in your box).
b. If you wanted to have at least 20 colored pencils left in your box, how many colored pencils would you have needed originally?
c. Write an inequality and show all steps for solving for x.
a. Let's define the variable x as the original number of colored pencils in your box.
You share them equally between you and your friend, so each of you gets x/2 colored pencils.
After sharing, you add 3 colored pencils to your own box, making the total number of colored pencils in your box (x/2) + 3.
Since the total number of colored pencils in your box is given as 15, we can write the equation as:
(x/2) + 3 = 15
To solve for x, we can first subtract 3 from both sides of the equation:
(x/2) = 12
Next, we can multiply both sides of the equation by 2 to isolate x: x = 24
b. To determine the number of colored pencils you needed originally to have at least 20 left, we can set up the following equation:
(x/2) + 3 >= 20
To solve for x, we can first subtract 3 from both sides of the equation:
(x/2) >= 17
Next, we can multiply both sides of the equation by 2 to isolate x: x >= 34
Therefore, you would have needed at least 34 colored pencils originally to have at least 20 left.
c. The inequality we set up in part b was:
(x/2) + 3 >= 20
To solve for x, we can follow these steps:
1. Subtract 3 from both sides of the inequality: (x/2) >= 17
2. Multiply both sides of the inequality by 2 to isolate x: x >= 34
So, the solution to the inequality is x >= 34, meaning the original number of colored pencils in your box needs to be at least 34 to have at least 20 left.
WRONG WRONG WRNO ONRzgnuhbtjymgvnb
I apologize if there was an error in my previous response. Please let me know where the mistake occurred so I can correct it.
c is wrong
Apologies for the mistake in the previous response. Let's solve part c correctly.
c. If we want to find an inequality for the original number of colored pencils, let's consider the scenario where you want to have at least 20 colored pencils left in your box.
After sharing equally with your friend, each of you will have x/2 colored pencils. Adding 3 more colored pencils to your own box gives you (x/2) + 3 colored pencils.
To have at least 20 colored pencils left, we can set up the following inequality:
(x/2) + 3 >= 20
To solve for x, we can subtract 3 from both sides of the equation:
(x/2) >= 17
To remove the fraction, we can multiply both sides of the inequality by 2:
2 * (x/2) >= 2 * 17
x >= 34
Therefore, the correct inequality is x >= 34. This means the original number of colored pencils in your box needs to be at least 34 to have at least 20 left.
NO THATS THE ANSWER TOO B ANSWER C
Apologies for the confusion. Let's solve part c correctly this time.
c. If we want to write an inequality for the original number of colored pencils, let's consider the scenario where you want to have at least 20 colored pencils left in your box.
After sharing equally with your friend, each of you will have x/2 colored pencils. Adding 3 more colored pencils to your own box gives you (x/2) + 3 colored pencils.
To have at least 20 colored pencils left, we can set up the following inequality:
(x/2) + 3 >= 20
To solve for x, we can subtract 3 from both sides of the inequality:
(x/2) >= 17
To remove the fraction, we can multiply both sides of the inequality by 2:
2 * (x/2) >= 2 * 17
x >= 34
Therefore, the correct inequality is x >= 34. This means the original number of colored pencils in your box needs to be at least 34 to have at least 20 left.