# Lola's Sweet Sixteen!

## Situation:

Becka is throwing her younger sister Lola a sweet sixteen birthday party. She only has \$650 to spend and she is inviting 50 people. The Exotic Banquet Hall charges an initial fee of \$300 and \$7 for each person that attends. The Magic Banquet Hall charges an initial fee of \$500 and \$5 for each person that attends. Which banquet hall will meet her requirements? And at what number of guests will both banquet halls charge the same amount?

The significance of the solution of this linear system is that the point of intersection, (100,1000), represents when both banquet halls will charge the same amount for the same number of guests. This means that for 100 guests, both banquet halls will charge \$1000. For an event with less than 100 guests, the Exotic Banquet Hall is cheaper. For an event with more than 100 guests, the Magic Banquet Hall is cheaper. For an event with exactly 100 guests, both banquet halls cost the same amount.

## Summary Statement:

Therefore, the Exotic Banquet Hall will meet Becka's requirements, and for an event with 100 guests, both banquet halls will charge the same amount, which is \$1000.