how many teenagers were originally going to split the pizza?

Question

the teenagers in a youth group are going to share the cost of some pizzas.  The original cost was $6 per person, but 5 teenagers couldn't stay to eat.  so the cost went up to $8 per person for the same total cost.  how many teenagers were originally going to split the pizza?

Answer 1

Let P = the price of the pizzas and let n = the original number of teenagers.  For n teenagers:

 

P = n*($6)

 

After 5 teenagers leave (assuming the same total cost, P):

 

P = (n-5)*($8) = 8n-40

 

Since the two equations both equal P, set them equal:

 

6n = 8n - 40

 

Solve for n