StudentShare solutions
Triangle menu

Solving Mathematical Problems - Math Problem Example

Not dowloaded yet

Extract of sample
Solving Mathematical Problems

At the top of my diagram I had colored five colored dots represent each person in the room. The first person was the red dot. The first person can't shake hands with himself but can shake hands with everyone else. So under the red dot I put a blue dot, a green dot, a yellow dot, and a purple dot. The second person can't shake hands with themselves and already shook hands with the first person. Under the blue dot I put a green dot, a yellow dot, and a purple dot. The third person can't shake hands with themselves and they already shook hands with the first two people. I put a yellow dot and a purple dot under the green dot. The fourth person can't shake hands with themselves and they already shook hands with the first three people, so I only put a purple dot under the yellow dot. Now the fifth person shook hands with everyone, so I didn't put any dots under the purple dot. I counted the dots in each column under the 5 dots on top and added them together to get a total of 10 handshakes. This is what my diagram looked like.
After I made this diagram I noticed a pattern. When there were five people in the room I added up all the numbers under 5, so it was 4+3+2+1. When there were six people in the room I added up all the numbers less than 6, so it was 5+4+3+2+1. ...
I used this rule to see how many handshakes there would be with even more people.

By looking at all these numbers I noticed a shortcut. Every time you go to find the number of handshakes for one more person in a room, you just add one less than the total number of people to the previous total number of handshakes. Using this rule to find the number of handshakes for 14 people you can add 13 to 78, which is 91. That's a lot easier than adding 13+12+11+10+9 and so on all over again.
Another pattern I noticed is that the number of handshakes for 5 people was 5 times 2, the number of handshakes for 6 people was 6 times 2.5, the number of handshakes for 7 people was 7 times 3, and the number to be multiplied kept increasing by half. To find out how many handshakes would happen in a room with 100 people, maybe I could use this rule to see what number I should multiply 100 by, instead of adding 100+99+98+97 and so on all the way down to 1. I started another table to see what number I needed to multiply 100 by.

Once I got to 21 I saw from the numbers in the table that you can get the number to multiply by subtracting one from the number of people then dividing by two. For 100 people in the room, then, you can subtract 1, which is 99, then divide by 2, which is 49.5. This means that to see how many handshakes would happen in a room of 100 people you just have to multiply 100 times 49.5. The total number of handshakes is 4950.
Even though patterns make things a lot easier, they aren't good if they aren't accurate. To make sure my rule was right I used a calculator to add 99+98+97+96 and so on all the way down to 1. Sure enough, it added up to 4950. ...Show more

Summary

If I was in a room with 4 other people and wanted to shake everyone's hand, four handshakes would happen. It gets trickier though if I wanted to know how many handshakes there would be if everyone wanted to shake everyone else's hand once. By using diagrams to find out how many handshakes would happen for different numbers of people, a pattern might be found…
Author : watsicawalker
Solving Mathematical Problems essay example
Read Text Preview
Save Your Time for More Important Things
Let us write or edit the math problem on your topic
"Solving Mathematical Problems"
with a personal 20% discount.
Grab the best paper

Related Essays

Problem Solving-Research Paper
For the results of the study conducted on the sample to be held true for the entire population, the sample should be a representative sample – that is, it should possess the same characteristics as the entire population, or as close to it as possible. A statistic is a characteristic that describes a sample; a parameter is a characteristic that describes a population.
3 pages (750 words) Math Problem
Algebra Math Problem
Application: Matthew would like to put up a small coffee-bean store selling two special varieties of coffee – Arabica(M) and Robusta(H). He estimates obtaining profit from each kg of Arabica(M) worth $10.50 and from each kg of Robusta(H) costing $9.25. If he desires to have 2500 kgs of bean-mixture sold for $9.74 per kg, how much of each kind must be present in the mixture?
6 pages (1500 words) Math Problem
Analyse and model engineering situations and solve problems using Ordinary differential equations
Analyse the cooling process. Based on real life experience, an object subjected to heat and eventually placed in a region of lower temperature naturally undergoes cooling. In its heated state, we know that such object contains energy which flows out of it once there occurs temperature difference between it and the environment within which it is exposed.
7 pages (1750 words) Math Problem
Analyse and model engineering situations and solve problems using Ordinary differential equations
Analyse the cooling process. As observed in reality, when such heated object is allowed to cool in a room, the object with an initially high temperature cools to an extent when its temperature becomes relatively bearable to the sense of touch, or that is to say towards a temperature at which the room is similarly felt.
10 pages (2500 words) Math Problem
Mathematical Modelling
The questions apply the accurate descriptions of the motion under various motions of situations. The work also introduces a lot of results and notions that are equally applicable in things that oscillate and vibrate in similar manner. For instance, the current analysis in fundamental circuit is analogous to analysis involving the spring’s mass.
4 pages (1000 words) Math Problem
Mathematical Tasks
These latter problems may be tricky and hard to conceptualize but with a clear basis and knowledge of different types of problems and techniques to apply, they can be solved easily. According to Chapter 2, task 2.2.1 on similarities and ratio, so many mathematical tasks can be developed and solved.
8 pages (2000 words) Math Problem
Differential Equation problems
3 pages (750 words) Math Problem
Computer Methods
4 pages (1000 words) Math Problem
College Math
I was puzzled to find out that the vectors connecting the same two points (let's say QR and RQ) are not equivalent. How can it happen It seems so logical to assume that if two endpoints are the same, the segment between them is the same also. Can somebody help me with this issue
2 pages (500 words) Math Problem
Theorem of Pythagoras in Mathematics
If we read the history of Pythagoras we would come to know his influence upon other philosophers like Plato's whole theory is very much affected by his thinking about geometry. He develops it in books VI and VII of the Republic, and says that "what we are talking about in geometry and mathematics, which are generally abstract entities of timeless, spaceless, and impersonal theologies.
12 pages (3000 words) Math Problem
Get a custom paper written
by a pro under your requirements!
Win a special DISCOUNT!
Put in your e-mail and click the button with your lucky finger
Your email
YOUR PRIZE:
Apply my DISCOUNT
Comments (0)
Rate this paper:
Thank you! Your comment has been sent and will be posted after moderation