# Bombay Palace vs. The Grand Olympia

### Which banquet hall provides a better deal?

## Introduction

Jonathan McMaster and Lily Kaur are having secular wedding. The couple don't want the wedding to have too many guests with very expensive prices. The couple want a banquet hall that provides good service while the cost being affordable. There are around 200 people coming for the wedding, Jonathan and Lily's budget is $25,000. They research on all the banquet halls in London, they finally decide on 2 banquet halls ; Bombay Palace and The Grand Olympia. But unfortunately Jonathan prefers The Grand Olympia and Lily prefers Bombay Palace, they both are arguing which one is better, we now have to help the couple decide which banquet hall is better and why.

## How do we solve this dispute?

## Services and Costs

__Bombay Palace__

**Wedding Package **

* Flat fee of $1000

( Flat fee of 1000 dollars due to cost of renting the banquet hall for 1 day)

Standing- 500 persons

Seated- 310 persons

Catering - $80 per person

**The Grand Olympia**

**Wedding ****Package**

*Flat fee of $890

( Flat fee of 890 dollars due to cost of renting the banquet hall for 1 day)

Standing- 500 persons

Seated- 310 persons

Catering- $100 per person

## Mathematically Solving this Dispute

**We can solve this dispute mathematically between the couple by evidence.**

**Let c represent the cost and p represent the number of people attending the wedding.**

__Bombay Palace__

There is a flat fee of 1000 dollars with catering of $80 per person.

In mathematical terms, this would look like;** c = 80p + 1000.**

__The Grand Olympia__

There is a flat fee of 890 dollars with catering of $100 per person.

In mathematical terms, this would look like; **c ****= 100p + 890.**

__Ax + By = C__

Bombay Palace: -80p + c = 1000

The Grand Olympia : -100p + c = 890

## Table Of Values

## Point of intersection

1: y = 80x + 1000

2:y= 100x + 890

We need to find the point of intersection ( or POI for short), hence let us substitute equation 1 to equal to equation 2 to find the value of x ( which is number of people attending the wedding).

80x + 1000 = 100x + 890

80x - 100x = -1000 + 890

-20x/ -20 = -110/ -20

Therefore, x = 5.5. But there is a problem, 5.5 people cannot attend the wedding obviously hence we will, in this context have to round it to 6 people.

To find the cost for "5.5 people" who attend the wedding, we will substitute the value of x in the equation to find the value of y.

y = 80( 5.5 ) + 1000

y = 440 * - This is the cost for "5.5 people" attending, excluding the flat rate since

practically speaking, there are still more people yet to come,but I will

still show the cost including the flat rate.

y = 440 + 1000

y = 1440

Now, I will confirm if the cost is the same at the same number of people for both banquet halls.

__Bombay Palace__

c = 80p + 1000

1440 = 80( 5.5 ) + 1000

1440 = 440 + 1000

1440 = 1440

Check!

**The Grand Olympia**

c = 100p + 890

1440 = 100( 5.5 ) + 890

1440 = 550 + 890

1440 = 1440

Check!

X is the number of people attending the wedding because number of people attending the wedding are independent of the cost of the wedding while the cost depends on the number of people who attend the wedding (y).

* **Unfortunately the point of intersection on the graph is very early on, thus I couldn't actually show the intersection properly with same rate of data because even if I tried no software was allowing me to input that much amount of data, that's why just to show where they intersect early on in the graph I labelled 5.5 ( around 6 people where the 2 lines meet and have the same cost for the same number of people).**