a. To find the original number of colored pencils, we can set up the equation:
(x/2) + 3 = 15
First, we divide x by 2, since we are sharing the pencils equally. Then, we add 3 to account for the additional colored pencils. Finally, we set this equal to 15, since that is the total number of pencils after sharing and adding 3.
To solve for x, we can subtract 3 from both sides of the equation:
(x/2) = 12
Then, we can multiply both sides of the equation by 2 to isolate x:
x = 24
So, the original number of colored pencils in your box was 24.
b. If we wanted to have at least 20 colored pencils left in your box, we can set up the inequality:
(x/2) + 3 >= 20
First, we divide x by 2, since we are sharing the pencils equally. Then, we add 3 to account for the additional colored pencils. Finally, we set this greater than or equal to 20, since that is the minimum number of pencils we want to have left in the box.
To solve for x, we can subtract 3 from both sides of the inequality:
(x/2) >= 17
Then, we can multiply both sides of the inequality by 2 to isolate x:
x >= 34
Therefore, the original number of colored pencils you would have needed would be at least 34.
c. The inequality to solve for x would be:
(x/2) + 3 >= 20
Following the same steps as in part b, we can solve for x:
(x/2) >= 17
x >= 34
So, the inequality to solve for x is x >= 34.
16. 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.
(5 points)
1 answer