POW #14
Problem Statement
If you are given an obtuse triangle is it possible to fill the space of the triangle with acute triangles?
Right Angle: An angle that is 90 degrees exactly.
Obtuse Angle: An angle that is greater than 90 degrees but less than 180 degrees.
Acute Angle: An angle that is less than 90 degrees.
If you are given an obtuse triangle is it possible to fill the space of the triangle with acute triangles?
Right Angle: An angle that is 90 degrees exactly.
Obtuse Angle: An angle that is greater than 90 degrees but less than 180 degrees.
Acute Angle: An angle that is less than 90 degrees.
Solution
You can put 7 acute triangles inside an obtuse triangle. You can do it in more but this is the least number I could come up with. I care about the least because you can always cut something up into smaller and smaller pieces but it's more difficult and more impressive to find the bigger triangles.
You can put 7 acute triangles inside an obtuse triangle. You can do it in more but this is the least number I could come up with. I care about the least because you can always cut something up into smaller and smaller pieces but it's more difficult and more impressive to find the bigger triangles.
POW #13
Problem Statement
An absent-minded teller switched the dollars and cents when she cashed a check for Mr. Brown, giving him dollars instead of cents and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had exactly twice as much left as his original check. What was the amount of the check?
An absent-minded teller switched the dollars and cents when she cashed a check for Mr. Brown, giving him dollars instead of cents and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had exactly twice as much left as his original check. What was the amount of the check?
The next day as a class we decided to find an equation. With our table groups we had to come up with an equation that we thought would solve the problem. Our first try none of the formulas worked. After that Jocelyn narrowed it down to an equation that would make a number that would could make into cents and dollars. For example 10.50 or 3.45. My group had no idea what to do until Mannix at the last second came up with D+(C➗100). As a class we proved that this equation will always work. Next we had to make an equation that would find how much money there was after the teller switched dollars for cents and cents for dollars. The equation C+(D➗100) was quickly found and decided on. After that Jocelyn showed us how to make an equation that would solve this problem. Or at least help us to solve this problem. The equation is C+D➗100-.05=2(D+C➗100).
After we had the equation C+D➗100-.05=2(D+C➗100), we didn’t have to but all wanted to simplify it. The way we simplified the equation is very hard to explain in words so I am going to show what we did as a class to simplify it.
1.100(C+D➗100-.05)=(2D+C➗100) 100
2. 100c+D-5=200D+2C
-2C -2C
3. 98C+D-5=200D
-D -D
4. 98C-5=199D
➗199 ➗199
5. 98C-5➗199=D
The simplified equation is 98C-5➗199=D.
After we had the equation C+D➗100-.05=2(D+C➗100), we didn’t have to but all wanted to simplify it. The way we simplified the equation is very hard to explain in words so I am going to show what we did as a class to simplify it.
1.100(C+D➗100-.05)=(2D+C➗100) 100
2. 100c+D-5=200D+2C
-2C -2C
3. 98C+D-5=200D
-D -D
4. 98C-5=199D
➗199 ➗199
5. 98C-5➗199=D
The simplified equation is 98C-5➗199=D.
Now I had an equation I just didn’t know what numbers to plug in to get the answer I wanted. I knew the numbers would be somewhere between 1 and 100. I also new that the number would be the only one that was a whole number. The first thing I tired doing was plugging in multiples of 10. I got to 60 and thought it wouldn’t work because of the kinds of decimals I was doing. Next i just started trying 61 and 62. I was planing to go by 1s but I thought that would take too long. So instead I looked at the number 199. I thought the number would have to be a multiple of that number. Because of all the 9s I thought of doing 3,6, and 9, I started plugging in numbers that had. Quickly I realized that none of them went into 199 evenly. But still i thought they had the most chance. so I started just plugging in 3s. I went from 3-63. When I plugged 63 in for C I got that D=31. The only whole number. The answer to the question.
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Solution
The man gave the teller a check for $31.63. the teller gave him $63.31. I know my answer is correct because it is the only answer possible. Jocelyn said the answer was the only whole number and so this has to be the only answer.
Evaluation
This problem was really hard for me. If we hadn't done it as a class I know I would have not been able to figure it out. My brain doesn’t really like turning things into equations so I would have just tried to guess numbers together to find it. I would have never guess 63 to check or 31. 31 is my one of my least favorite numbers so I would never check it.
The man gave the teller a check for $31.63. the teller gave him $63.31. I know my answer is correct because it is the only answer possible. Jocelyn said the answer was the only whole number and so this has to be the only answer.
Evaluation
This problem was really hard for me. If we hadn't done it as a class I know I would have not been able to figure it out. My brain doesn’t really like turning things into equations so I would have just tried to guess numbers together to find it. I would have never guess 63 to check or 31. 31 is my one of my least favorite numbers so I would never check it.