Answer to Question #167932 in Algebra for Ali

Question

You are a Grade 10 representative on the student council and you have been assigned the task of finding a location to House of dance for students of CISE you have narrowed it down to three options which are outlined below.

ancient abyss is a location that charges a flat fee of $200 and $4 dollars per person, beautiful babylon is a location that charges a $99 flat fee and $6 per person, crazy Cleoparta is a location that charges $280 flat fee and $3 per person you will analyze the three options and put together a proposal to submit to the student council outlining your recommendations

Answer 1

Let $n=$ the number of students.

Ancient abyss: $C_A(n)=200+4n$

Beautiful babylon: $C_B(n)=99+6n$  

Crazy Cleoparta: $C_C(n)=280+3n$  

$$200+4n=99+6n=>n=50.5$$

For $n\le50$

$$C_B<C_A<C_C$$

$$280+3n=99+6n=>n=60\dfrac{1}{3}$$

For $51\leq n\le60$

$$C_A<C_B<C_C$$

$$200+4n=280+3n=>n=80$$

For $51\leq n\leq79$

$$C_A<C_C<C_B$$

For $n=80$

$$C_A=C_C<C_B$$

For $n>80$

$$C_C<C_A<C_B$$