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.
make a short answer
a) Let's solve for x (the original number of pencils):
Step 1: Share the pencils equally between you and your friend. This means each of you will get x/2 pencils.
Step 2: Add 3 more pencils to your own box.
Step 3: The total number of pencils you have now is (x/2) + 3.
Step 4: According to the problem, this total is 15, so we can write the equation:
(x/2) + 3 = 15
Step 5: To isolate x, we subtract 3 from both sides of the equation:
(x/2) + 3 - 3 = 15 - 3
(x/2) = 12
Step 6: Finally, we multiply both sides of the equation by 2 to solve for x:
2 * (x/2) = 12 * 2
x = 24
b) If you wanted to have at least 20 pencils left in your box, you would need to find the original number of pencils, x:
Step 1: Subtract 20 from the total number of pencils you have after sharing and adding 3 (which is 15):
x - 20 ≥ 15
Step 2: To isolate x, we add 20 to both sides of the inequality:
x - 20 + 20 ≥ 15 + 20
x ≥ 35
Therefore, you would need to have originally at least 35 pencils in your box.
c) The inequality representing the condition of having at least 20 pencils left in your box is:
x - 20 ≥ 15
make a shorter answer
a) x/2 + 3 = 15
x = 24
b) x - 20 ≥ 15
x ≥ 35
c) x - 20 ≥ 15
Which object will have particles with the highest average kinetic energy?(1 point)
Responses
water at 40°C in a swimming pool
water at 40°C in a swimming pool
water at 37°C in a glass
water at 37°C in a glass
an iceberg at 0°C
an iceberg at 0°C
a drop of water at 90°C
The drop of water at 90°C will have particles with the highest average kinetic energy.
a) Let's solve part a) step by step:
Step 1: Let's assume the original number of pencils in your box is x.
Step 2: You share them equally with your friend, which means you both get x/2 pencils each.
Step 3: You add 3 more pencils to your own box, resulting in x/2 + 3 pencils for you.
Step 4: The total number of pencils you have after sharing and adding is 15, so we can write the equation as follows:
x/2 + 3 = 15
Step 5: To solve the equation, we'll subtract 3 from both sides to isolate the term with x/2:
x/2 = 12
Step 6: Finally, we'll multiply both sides by 2 to get the value of x:
x = 24
Therefore, the original number of pencils in your box was 24.
b) If you wanted to have at least 20 pencils left in your box, let's solve part b):
Step 1: Let's still assume the original number of pencils in your box is x.
Step 2: After sharing equally with your friend, you both have x/2 pencils each.
Step 3: You add 3 more pencils to your own box, resulting in x/2 + 3 pencils for you.
Step 4: To have at least 20 pencils left, we can write the inequality as follows:
x/2 + 3 ≥ 20
Step 5: To solve the inequality, we'll subtract 3 from both sides to isolate the term with x/2:
x/2 ≥ 17
Step 6: Finally, we'll multiply both sides by 2 to get the value of x:
x ≥ 34
Therefore, you would have needed at least 34 pencils originally to have at least 20 pencils left in your box.
Short answer:
a) The original number of pencils in your box was 24.
b) You would have needed at least 34 pencils originally to have at least 20 pencils left in your box.
a) Let's break down the problem step by step.
Step 1: You start with x colored pencils in your pencil box.
Step 2: You share them equally with your friend, so each of you gets x/2 colored pencils.
Step 3: You add 3 pencils to your own box, so you will have x/2 + 3 colored pencils in your box.
According to the problem, you end up with a total of 15 colored pencils in your box. So, we can write the equation:
x/2 + 3 = 15
To solve the equation and find the original number of pencils in your box, we can follow these steps:
Step 1: Subtract 3 from both sides of the equation:
x/2 = 12
Step 2: Multiply both sides of the equation by 2 to cancel out the division by 2:
2 * (x/2) = 2 * 12
x = 24
Therefore, the original number of 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 as follows:
x/2 + 3 ≥ 20
To solve for x, we can follow these steps:
Step 1: Subtract 3 from both sides of the equation:
x/2 ≥ 20 - 3
x/2 ≥ 17
Step 2: Multiply both sides of the equation by 2 to cancel out the division by 2:
2 * (x/2) ≥ 2 * 17
x ≥ 34
Therefore, the original number of pencils needed in your box would be at least 34.
c) The inequality representing the problem is x/2 + 3 ≥ 20.