**KOBAYASHI**

Background

Both

Kobayashi

and

Sonya

are world champion hotdog eaters. In this MasterCard advertisement,

Kobayashi

is approached by

Sonya

at a corner store. At this point,

Kobayashi

orders one hotdog. After which,

Sonya

orders two. They both order one more than each other each round for a total of four rounds until there is none left on the grill.

Who is ahead by the end of round 20 and by how many?

Based on observations from the table of values,

Sonya

will be ahead of

Kobayashi

by 1 hot dog each round, adding up to a total of 20 hot dogs by round 20.

Therefore we can use the formula

1 x n

where 1 represents how many hot dogs

Sonya

is ahead by after each round and 'n' represents the round number.

How can we determine how many hot dogs each person ordered in round 20?

We began by creating a table of values. Can you see a pattern?

By observing the values of the table, we observed that the round number is half of the number of hotdogs

Sonya

orders during that round.

Thus: #

Sonya

orders = 2n

At every round, the number

Kobayashi

ordered was one less than that of Sonya.

Thus: #

Kobayashi

orders = 2n - 1

To determine how many each person ordered in round , we can now use our formula.

n

#

Sonya

orders = 2

So, How many hotdogs does each person order in round 20?

= 2 ( )

20

= 40

#

Kobayashi

orders = 2 - 1

n

n

= 2 ( ) - 1

20

= 39

How many hotdogs have they eaten after the 20th round?

Sonya

eats just as much as

Kobayashi

along with one added hot dog each round. Since the number of hotdogs

Sonya

is up by in a round is equal to n,

Sonya's

total can be described with the formula

=

n^² + n

What have we learned?

MATH IS EVERYWHERE!

As tough as it is to accept for some, mathematics doesn't end when you set foot outside of the classroom. This video was a great example. When we watch advertisements, the last thing we would think about is applying math to the concept. THE MATH IS OUT THERE!

It may not always be simple, but you just need to open your eyes!

**vs.**

**SONYA**

Who will be the ultimate

By:

Franco Prieto

,

Tanvir Khaira

Nishchit Gautam

&

Amandeep Bamrah

How many hotdogs are on the grill at the start?

Because the video lasted for only four rounds, we can use our formula to determine how many each person ordered in total by round four and add the two to get a total

Kobayashi

= 4^2

Sonya

= 4^2 + 4

Total=

36

Alternatively, you can attempt to use the very blurry image above.

Total = (4^2) + (4^2 + 4)

= (16) + (20)

constant; by round 2 he has eaten 3 hot dogs plus the one from round one, for a total of 4 hot dogs. These values are all perfect squares reached by squaring the round number. If you square the n round you get the total number of hot dogs

Kobayashi

has eaten by the end of that round.

Searching for a relation between the round number and total number of hot dogs eaten by

Kobayashi

, we realized the sum of the total number of hot dogs he eats is always a perfect square which can be achieved by squaring the round number

= n^²

. In other words, if you add the number of hot dogs

Kobayashi

has eaten in total by round 1 you get 1, which is a perfect square. This pattern is

Therefore:

Kobayashi total = n^²

Sonya

total = n^² + n

WEINER!

Thus:

# of hotdogs Sonya is ahead after round n = n

For example, when Sonya is in round 5, she orders 10. In round 6, she orders 12.

Can you determine how many she will order in round 7? How about round 14?

So, if we know Sonya ordered 10 in round 5 Kobayashi ordered 9. Likewise, if she ordered 12 in round 6, he ordered 11.

How much will he order in round 7?