A teacher from Anderson Middle School printed k nametags in preparation for the science fair. Half of the nametags were given out to students and 100 nametags were given out to parents. Three-fifths of the remaining nametags were given out to teachers and contests judges. How many nametags were not given out?
Thank You
tags given to students and parents = k/2 + 100
tags remaining = k - (k/2+100)
= k/2 - 100
tags given to teachers and judges
= (3/5)(k/2 - 100)
so tags not given out
= (2/5)(k/2 - 100)
= k/5 - 40
check:
assume they had 600 namtags
according to my expression,
600/5 - 40 or 80 were not given out
let's see:
given to students and parents
= 300+100 = 400
leaving 200
3/5 of 200 or 120 were given to teachers and judges,
leaving 80 not handed out
There is a very high probability that my answer is right.
Well, let's see. If k nametags were printed, half of them were given out to students, which means k/2 nametags were in the hands of the young scholarly minds. Then, an additional 100 nametags were handed out to parents, bringing the total to k/2 + 100 nametags drifting around.
Now, here's where things get a bit funny. Three-fifths of the remaining nametags were given out to teachers and contest judges. So, that leaves us with (k/2 + 100) * (2/5) nametags that are still gracing the world with their presence.
To find out how many nametags were not given out, we subtract the total number of vanished nametags from the original k. So, the number of nametags not given out is k - [(k/2 + 100) * (2/5)].
I hope this doesn't give you "tag-mare" nightmares!
Let's break down the problem step-by-step:
1. The teacher printed k nametags.
2. Half of the nametags were given out to students. So, k/2 nametags were given out to students.
3. 100 nametags were given out to parents.
4. The remaining nametags can be found by subtracting the nametags given to students and parents from the total number of nametags: k - (k/2 + 100).
5. Now, three-fifths of the remaining nametags were given out to teachers and contests judges. So, the number of nametags given out to teachers and contests judges can be found by multiplying the remaining nametags by 3/5: (k - (k/2 + 100))(3/5).
6. The number of nametags not given out is the difference between the remaining nametags and the nametags given out to teachers and contests judges: (k - (k/2 + 100)) - (k - (k/2 + 100))(3/5).
7. Simplifying this expression will give us the final answer.
Let's simplify the expression for the number of nametags not given out:
(k - (k/2 + 100)) - (k - (k/2 + 100))(3/5)
= (k - k/2 - 100) - (k - k/2 - 100)(3/5)
= (k/2 - k/2) - 100 - (3/5)(k - k/2 - 100)
= -100 - (3/5)(-k/2 - 100)
= -100 + (3/5)(k/2 + 100)
= -100 + (3k/10 + 300)
= 3k/10 + 200
Therefore, the number of nametags that were not given out is 3k/10 + 200.
To find out how many nametags were not given out, let's break down the information step by step:
1. The teacher printed "k" nametags in preparation for the science fair.
2. Half of the nametags were given out to students. So, "k/2" nametags were given out to students.
3. 100 nametags were given out to parents.
4. The remaining nametags would be "k - (k/2 + 100)".
5. Three-fifths of the remaining nametags were given out to teachers and contest judges. So, "(3/5) * (k - (k/2 + 100))" nametags were given out.
6. The number of nametags that were not given out can be calculated by subtracting the given-out nametags from the total nametags printed: "k - (k/2 + 100) - (3/5) * (k - (k/2 + 100))".
Simplifying the expression:
"k - (k/2 + 100) - (3/5) * (k - (k/2 + 100))"
"k - k/2 - 100 - (3/5) * (k - k/2 - 100)"
"k - k/2 - 100 - (3/5) * (k/2 - 100)"
"k - k/2 - 100 - 3/10 * (k/2 - 100)"
"(2k - k)/2 - 100 - 3/10 * (k/2 - 100)"
"k/2 - 100 - 3/10 * (k/2 - 100)"
"simplifying further is not possible without a specific value for k"
Therefore, the expression to calculate the number of nametags that were not given out is "k/2 - 100 - 3/10 * (k/2 - 100)". If you provide a specific value for k, we can find the solution.