Diophantus's Riddle

This is Diophantus's riddle it wants you to solve to find out how old Diophantus is when he dies. This riddle is somethings that many people don't want to work on because it has the awful fraction that everyone hates but as you work through it the fraction all start to work out and work together. Once you work through it you come to a whole final number. The following is my work on solving this problem.

If D equals Diophantus's age and S is the age of his son you will get the following expressions:

These numbers come from the riddle:

       

 is how long he spends as a boy

 is his life with a bread

 his life before marriage 

5 years married without child 

4 years after his son died till he died

Now doing the parenthesis first:

Find the common denominator witch is 84 we get 

(14/84)+(7/84)+(12/84)=(33/84)

(33/84) D+S+9

Replace S with (1/2)D and since we know that (42/84) is the same as (1/2) we can replace that as well

(33/84)D+(42/84)D+9=D

(75/84)D+9=D

Move that D's to the same side,

9=(9/84)D

84=D

Even though it isn't asked for we can now find the son's age by using 84 in our equation for S.

(1/2)(84)=S=42

So taking what we have just gone through it's time to make our own and since we are all math nerds I will use "messier" fractions. I will being doing this in steps, stick with the steps. 

Step 1: Pick proportion.

   (1/8),(1/20),(1/15) 

   I found what their common denominator is.

(15/120),(5/120),(8/120)

Step 2: Variables and additional data.

   S=spending

   B=Balance

Step 3:Write the problem

   You're going shopping with your friends and you find your favorite band is selling concert tickets for 1//8 your total bank balance. Continuing shopping you find the best outfit and shoes for the concert which cost 1/15 and 1/20 respectively of you balance. Once you get home you look and see that you have 18/30 of what you started with plus the $10 you have left from lunch. How much did your bank balance start at?

Step 4: Check!

   B=(1/8+1/15+1/20)B+S+10 

S=(18/30)

1/8-concert tickets

1/15-outfit

1/20-shoes

S-how much left 

10-your change

Common denominator.

15/120+5/120+8/120=28/120

B=(28/120)B+S+10

Plug in S.

B=(28/120)B+(18/30)B+10

Common denominator.

(28/120)+(72/120)=97/120

B=(100/120)B+10

(20/120)B=10

Multiply the reciprocal of (20/120) to both sides.

(120/20)(20/120)B=10(120/20)

B=(120/10)

B=60

That is the final step and since we found a real answer that makes sense with the question asked we have a successful problem to make it more we could always ask:

   How much were the tickets?

   How much was the outfit?

   How much were the shoes?

This is how I worked through the Diophantus's riddle but there are many different ways to do it. Whats your's?

   This problem makes me wonder what else can be shown to students in better ways. This problem is a very good way of showing how fraction can work and correspond to problems that are strictly fraction heavy. I know that during high school I like many other hated fractions and this type of problem I think would help student make a connection to fraction. We all know that once students have a connection to what they are learning then they will not only learn it easier but have a better chance of remembering what they have learned.  

5 milestones of Math

What is math? This is a question that has been asked, you would think that being at the end of our math degrees we would have an answer to this but it is the most difficult question. So through this class and this blog I will be creating/thinking/learning what I believe the answer to this question is.

In the history of math there has been many major discoveries, but what are some of the main most important ones. I believe an important one would be discovery of infinity. This was a hard topic for many people to understand and even accept but is the most well known today. I think that without it there would be a completely different math world out there.

Throughout my college career I had to take Euclidean Geometry, which was unlike any other math class I have taken because it makes you think about things you can't automatically see or understand. The idea that there are more then just what we know as Geometry was a wide awakening to me. Which bring me to thinking that this is another major discovery in math of Euclidean.

We would have gotten no where in math without the basic operations of adding and subtraction. To me this was the very beginning of people learning and putting words with what they are doing. There are so many area of life that use these ideas and it to me would be the first and most important discovery.  

  Leading off of adding and subtracting I believe that multiplication and division would also be very important in our math history. Yes it is built of adding and subtracting but being able to use these idea really made math a more universal tool. 

Finally I think that in math when it comes to milestones that we need to know how to communicate what we know to others outside the math world. I believe that over the years we have become better and continue to get better at how it is communicated. I believe that milestone to be the opening up of the math word to the normal person.