# Which Hall Should TFSS Choose?

## The TFSS school council's problem

Turner Fenton wants to throw their school dance on January 20th and they have not decided what banquet hall to have it at. They don't know how many kids are exactly coming but, want to know which hall is cheaper for how many kids.

## The Prices of Two Different Banquet Halls

Chand banquet hall's prices are \$30 per student plus a fixed price of \$1000

Saag banquet hall's prices are \$20 per student plus a fixed price of \$1800.

## Equations For Both of The Banquet Halls

Let X represent number of people

Let Y represent total cost

Let B represent fixed price

Chand Banquet Hall:

y=mx + b

y=30x + 1000

Saag Banquet Hall:

y=mx + b

y=20x + 1800

This graph shows the y axis as the cost (dependant variable) and the x axis as the amount of kids attending (independent variable). According to the graph, at 80 kids both banquet halls will cost the same and after 80 kids Saag banquet hall is cheaper, before 80 kids Chand banquet hall is cheaper.

## Non-Graphic Solution

30x+1000=20x+1800

10x=800

10x/10=800/10

x=80

*To check if the math is correct*

30x+1000=20x+1800

30(80)+1000=20(80)+1800

3400=3400

## Therefore at 80 students both banquet halls will cost \$3400, after 80 students Saag banquet hall is cheaper and before 80 students Chand banquet hall is cheaper.

*all banquet hall names and prices are fictitious*