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 represent the given information:
(x/2) + 3 = 15
To solve for x, we need to isolate x.
First, let's get rid of the division by multiplying both sides of the equation by 2:
2 * (x/2) + 2 * 3 = 2 * 15
This simplifies to:
x + 6 = 30
Next, let's isolate x by subtracting 6 from both sides:
x + 6 - 6 = 30 - 6
This simplifies to:
x = 24
Therefore, the original number of pencils in your box was 24.
b) To find out how many pencils you would have needed originally in order to have at least 20 pencils left, we can set up an inequality.
Let's represent the original number of pencils as y:
(y/2) + 3 >= 20
To solve for y, we need to isolate y.
First, let's get rid of the division by multiplying both sides of the inequality by 2:
2 * (y/2) + 2 * 3 >= 2 * 20
This simplifies to:
y + 6 >= 40
Next, let's isolate y by subtracting 6 from both sides:
y + 6 - 6 >= 40 - 6
This simplifies to:
y >= 34
Therefore, you would have needed at least 34 pencils originally in order to have at least 20 pencils left.
c) The inequality representing this situation is:
(x/2) + 3 >= 20
To solve for x, we need to isolate x.
First, let's get rid of the division by multiplying both sides of the inequality by 2:
2 * (x/2) + 2 * 3 >= 2 * 20
This simplifies to:
x + 6 >= 40
Next, let's isolate x by subtracting 6 from both sides:
x + 6 - 6 >= 40 - 6
This simplifies to:
x >= 34
Therefore, the original number of pencils in your box should be greater than or equal to 34 in order for you to have at least 20 pencils left.
are you sure
Apologies for the incorrect responses in my previous answer. Let's solve the problem correctly:
a) Let's denote the original number of colored pencils as x.
When you share them equally with your friend, each of you will have x/2 colored pencils.
After adding 3 more colored pencils to your own box, you have x/2 + 3 colored pencils.
According to the given information, x/2 + 3 = 15.
To solve for x, we can isolate x by subtracting 3 from both sides:
x/2 = 15 - 3,
x/2 = 12.
Then multiply both sides by 2 to eliminate the division:
2 * (x/2) = 2 * 12,
x = 24.
Therefore, the original number of colored pencils in your box was 24.
b) If you want to have at least 20 colored pencils remaining, we can set up an inequality:
(x/2) + 3 >= 20.
To solve for x, we need to isolate x.
Subtracting 3 from both sides of the inequality, we have:
(x/2) >= 20 - 3,
(x/2) >= 17.
To eliminate the division by 2, we multiply both sides by 2:
2 * (x/2) >= 17 * 2,
x >= 34.
Therefore, you would have needed at least 34 colored pencils originally in order to have at least 20 colored pencils remaining.
c) The inequality representing this situation is:
(x/2) + 3 >= 20.
To solve for x, we need to isolate x.
Subtracting 3 from both sides of the inequality, we have:
(x/2) >= 20 - 3,
(x/2) >= 17.
To eliminate the division by 2, we multiply both sides by 2:
2 * (x/2) >= 17 * 2,
x >= 34.
Therefore, the original number of colored pencils in your box should be greater than or equal to 34 in order for you to have at least 20 colored pencils remaining.
a) Let's break down the steps to solve for x.
Step 1: Begin with the equation for the given situation.
x/2 + 3 = 15
Step 2: Subtract 3 from both sides of the equation.
x/2 = 12
Step 3: 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, x, was 24.
b) If you wanted to have at least 20 pencils left in your box, you can set up an inequality to solve for x.
Step 1: Create the inequality. Since we're looking for the original number of pencils, we can use the variable x.
x/2 + 3 ≥ 20
Step 2: Subtract 3 from both sides of the inequality.
x/2 ≥ 17
Step 3: Multiply both sides of the inequality by 2 to eliminate the fraction.
2 * (x/2) ≥ 2 * 17
x ≥ 34
Therefore, you would have needed at least 34 pencils originally to have at least 20 pencils left in your box.
c) The inequality is x/2 + 3 ≥ 20.
a) Let's break down the problem step by step:
Step 1: Share the pencils equally between you and your friend. After sharing, you and your friend each have x/2 colored pencils in your boxes.
Step 2: Add 3 more colored pencils to your own box. Now you have (x/2) + 3 colored pencils in your box.
Step 3: The total number of colored pencils is 15. So, we can set up the equation:
(x/2) + 3 = 15
Step 4: To solve for x, we will isolate x by subtracting 3 from both sides of the equation:
(x/2) = 15 - 3
(x/2) = 12
Step 5: To further isolate x, we can multiply both sides by 2:
2 * (x/2) = 2 * 12
x = 24
Therefore, the original number of colored pencils in your box was 24.
b) To determine how many pencils you would have needed originally to have at least 20 pencils left in your box, we can set up the following inequality:
(x/2) + 3 ≥ 20
Step 1: Subtract 3 from both sides of the inequality:
(x/2) ≥ 20 - 3
(x/2) ≥ 17
Step 2: Multiply both sides of the inequality by 2 to isolate x:
2 * (x/2) ≥ 2 * 17
x ≥ 34
Therefore, you would have needed at least 34 colored pencils originally to have at least 20 pencils left in your box.
c) The inequality we used in part b) can be expressed as:
(x/2) + 3 ≥ 20
Step 1: Subtract 3 from both sides of the inequality:
(x/2) ≥ 20 - 3
(x/2) ≥ 17
Step 2: Multiply both sides of the inequality by 2 to isolate x:
2 * (x/2) ≥ 2 * 17
x ≥ 34
Therefore, the inequality expression is x ≥ 34.