three trees on a golf course that Mr. Nemirov is playing.
Each of the trees will have at least 4 Blue Jays and 2 Orioles. However, no tree
may have more Orioles than Blue Jays in its branches.
Determine the largest number of birds that can be in one tree.
I'm still not too sure about the answer, but from what I came up with, I got 14....
ReplyDeleteSo I started by splitting the amounts as evenly as possible, and I got 5:5, 5:5 and 5:4, with the first part of the ratios being the blue jays, and the latter as the orioles. This is what I'm not too sure about, and that's whether or not it's allowed to have the same amount of blue jays and orioles on the same tree. The question stated that there could not be more orioles than blue jays, but it didn't mention whether or not there can be the same amount.... Let's just say in this question, there can be even amounts. So from 5:5, I took 1 from the blue jays, making 4, and 3 from the orioles, making 2, which is the least amount of birds there can be on a tree, and I added that to my other 5:5 tree, making 6:8. But now, there were more orioles, so I took one more blue jay from the last tree (5:4), and added that to my 6:8 tree, making it 7:8. It still wasn't even, so I knew I either had to match up or down. But if I matched up, my ratios on the other 2 trees wouldn't match the criteria. So I had no choice other than to match down. So I took 1 from 8, making it 7, and added that to my 4:2 tree ratio, making it 4:3. The biggest ratio I then had was 7:7, making a total of 14 birds.
To check, I looked at all my ratios, (4:3, 7:7, and 4:4) to see if I could add any more birds to my biggest number, without crossing the criteria. I could take one oriole from the first tree (4:3), because the least amount of birds could only be 4:2, but that would make my 7:7 ratio 7:8, which means that there would be more orioles than blue jays, which is unacceptable. I could have also taken 2 orioles from my last tree (4:4), but that leaded to the same situation as the first: there would be more orioles than blue jays. So that's how I knew the most amount of birds there could be on a tree was 14, or in a ratio, 7:7.
Good job Emily. I understand how and why you got your answer. It was well explained and I enjoyed reading it. I like how you assumed that there could be the same amount of Orioles to Blue Jays. Good work.
DeleteHi,
ReplyDeleteI think the largest number of birds that can be in a tree is 13 birds.
PROCESS:
Key:
BJ=Blue Jays
O= Orioles
To help me solve this question I drew pictures. I drew 3 trees and since I know that there are at least 4BJs and 2Os in each tree I wrote that in each tree. Then I added how much BJs there are so far in all 3 trees, I got 12BJs. Then I added all the Os in all three trees which gave me 6Os. Now I subtracted the original number of each of the types of birds with how much birds are on the tree so far.
1. First Tree Second Tree Third Tree Altogether
4BJ 4BJ 4BJ 12BJ (3 trees) 15 (original)
2O 2O 2O 6O (3 trees) 14 (original)
2. 15BJ (original) - 12BJ (3 trees) = 3BJ (left)
Now that I have found out there are 3 more blue jays left to be sorted out into the 3 trees I can start to sort them. I am trying to find the largest number possible so instead of sorting it out evenly, I put all 3BJs into one of the trees, the first tree. So this changes the amount of birds in the first tree, there are 7BJs and 2Os.
3. 14Os (original) - 6Os (3 trees) = 8Os (left)
Now that I know that there are 8Os left to be sorted out I can start to sort it out. I have to make sure that there are more BJs than Os in each tree but I have to find the largest amount of birds. Since I know that there are 7BJs in the first tree (the largest amount of BLUEJAYS in one tree) I subtracted 1 from 7 which gave me 6. That tells me that there should be 6Os in my first tree so that I could get the largest number of birds in a tree. There are 2Os in the first tree, my aim is 6Os in the first tree. So I took 4Os from the 8Os that were left to be sorted out and put them into the first tree. Then I split the amount of Orioles left to be sorted which now is 4Os with the other 2 trees (second tree and third tree). Which means for the other 2 trees 2Os go to each one, which finishes up the amount of Orioles left to be sorted out.
4. First Tree Second Tree Third Tree
7BJs 4BJs 4BJs
6Os 4Os 4Os
= 13 birds = 8 birds = 8 birds
REQUIREMENTS
- There are no trees where there are more Orioles than Blue jays
- Each tree has AT THE LEAST 4BJs and 2Os
Thats why I think that the largest number of birds (altogether) in a tree is 13 birds!
Thanks for reading my response.
Bye.
- Kajana.Y
Alright-y, y'all! How ya doing? My sister and I did this question together.
ReplyDeleteWe think that the largest number of birds that can be in one tree is 13. We got this answer by applying our knowledge of mathematical operations (addition/subtraction/multiplication) to this question.
Step #1. We arranged numbers into sections to distinguish the amount of birds in each tree. First, we started with the numbers 4 and 2 (the least amount of birds in one tree)
Step #2. We knew that the minimum was 4 & 2 in each tree and that the amount of Orioles cannot be greater than the Blue Jays. We also know that there are 15 Blue Jays and 14 Orioles. From here we tried to identify the largest amount of birds in one tree by using what we already know about each tree.
Step #3. We think that the largest amount of birds of one tree can be identified through *one* tree. Thus, we focused on finding the greatest number without equally distributing numbers among the other trees. Such as:
4,2...4,2...4,2
OR
8,4...8,4...8,4
We first identified the greatest value of BLUE JAYS:
15 (total) - 8 (4+4) = 7
Therefore, tree #1 has 7 BLUE JAYS
Then we identified the greatest value of ORIOLES:
We first tried 6 because it cannot be higher than blue jays (7).
6 + 4 (2+2) = 10 (which is incorrect because the value is 14)
14 - 6 = 8
Therefore, the 2 other trees have 4 ORIOLES each... the first tree has 6.
6 + 8 (4+4) = 14.
Our answer is correct because it follows the requirements and is the greatest value. Blue jays cannot go over 7 because it doesn't meet the minimum amount of birds/tree. Also, Orioles cannot go over 6 because it cannot be greater than Blue Jays.
My bad. We thought that the ratio of Orioles to Blue Jays could not be the same on each tree. Oppsies.
DeleteThe correct answer is in fact 14. Please see the above solution.
ReplyDelete