a) Let's solve for x, the original number of pencils in your box.
Step 1: Share the pencils equally with your friend. This means you divide the pencils by 2.
Step 2: After sharing equally, there are x/2 pencils left in your box.
Step 3: Add 3 more colored pencils to your own box.
Step 4: The total number of pencils in your box is now x/2 + 3.
Step 5: According to the problem, this total is 15. So we set up the equation:
x/2 + 3 = 15
Step 6: Subtract 3 from both sides of the equation to isolate x/2.
x/2 = 15 - 3
x/2 = 12
Step 7: Multiply both sides of the equation by 2 to solve for x.
(x/2) * 2 = 12 * 2
x = 24
Therefore, the original number of pencils in your box was 24.
b) To solve for the original number of pencils if you want to have at least 20 pencils left in your box:
Step 1: After sharing equally with your friend, you will have x/2 pencils left in your box.
Step 2: You add an additional 3 colored pencils to your box, so the total number of pencils will be x/2 + 3.
Step 3: According to the problem, you want to have at least 20 pencils left in your box, so we set up the inequality:
x/2 + 3 ≥ 20
Step 4: Subtract 3 from both sides of the inequality to isolate x/2.
x/2 ≥ 20 - 3
x/2 ≥ 17
Step 5: Multiply both sides of the inequality by 2 to solve for x.
(x/2) * 2 ≥ 17 * 2
x ≥ 34
Therefore, you would have needed originally at least 34 pencils in your box to have at least 20 left.
c) The inequality is x/2 + 3 ≥ 20.
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.
(5 points)
1 answer