a) Let's represent the original number of pencils in the box as x.
Step 1: Sharing equally between you and your friend means you each get x/2 colored pencils.
Step 2: Adding 3 more colored pencils to your box gives you x/2 + 3 pencils.
Step 3: The total number of pencils you have after sharing and adding 3 more is x/2 + 3 + x/2 = 15.
Step 4: Simplifying the equation:
x/2 + x/2 + 3 = 15
2x/2 + 3 = 15
x + 3 = 15
Step 5: Subtracting 3 from both sides of the equation:
x + 3 - 3 = 15 - 3
x = 12
Therefore, the original number of pencils in your box is 12.
b) If you want to have at least 20 pencils left in your box, let's represent the original number of pencils needed as y.
Step 1: Sharing equally between you and your friend means you each get y/2 colored pencils.
Step 2: Adding 3 more colored pencils to your box gives you y/2 + 3 pencils.
Step 3: The total number of pencils you have after sharing and adding 3 more is y/2 + 3 + y/2 = 20.
Step 4: Simplifying the equation:
y/2 + y/2 + 3 = 20
2y/2 + 3 = 20
y + 3 = 20
Step 5: Subtracting 3 from both sides of the equation:
y + 3 - 3 = 20 - 3
y = 17
Therefore, the original number of pencils needed in your box to have at least 20 left is 17.
c) The inequality representing the situation where you want to have at least 20 pencils left in your box is:
y/2 + 3 ≥ 20
Step 1: Subtracting 3 from both sides of the inequality:
y/2 ≥ 17
Step 2: Multiplying all terms by 2 (to get rid of the fraction):
2(y/2) ≥ 2(17)
y ≥ 34
Therefore, the original number of pencils needed in your box is greater than or equal to 34.
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 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
1 answer