**By: Camryn Paul, Lauren Mombille, and Selena Li**

**Lets Dance Project**

6x+(150/x)+(600/x) to find ticket cost for Band A, where x is the number of students.

7.25x+(150/x)+(350/x) to find ticket cost for Band B, where x is the number of students.

If 200 students attend the dance…

The cost of the tickets without the band would be $6.75 per ticket, to cover the catering expenses. With Band A, the cost would be increased to $9.75 per ticket. If Band B were to perform instead, it would cost the same if Band A were to perform, $9.75 per ticket. So, either band could perform in the case of 200 students.

If 300 students attend the dance…

The cost of the tickets without the band would be $6.50 per ticket, to cover the catering expenses alone. With Band A performing, the cost would increase to $8.50 per ticket. However if Band B performs, it would be $8.92. So, in the case of 300 students, Band A should perform instead.

Activity 3

Cost for 100 students: $750

Cost for 150 students: S1050

f+600=750

f=150

f+900=1050

Fixed cost=$150

Each person=$6

Activity 2

Band A - $600

Band B

m= 350+ 1.25t

600= 350 +1.25t

-350 -350

250= 1.25t

1.25 1.25

t=200

200 tickets need to be sold for both bands the equal the same amount.

Activity 1

m=600

m=350+1.25t

Band A charges $600 to play for the evening Band B charges $350 plus $1.25 per ticket sold

Finishing Project

Overall, a good ticket price could be $9.80, so that if 200 people or more were to attend, the costs would be covered and there would still be money earned. If about 200 or more people attend, the costs for dinner should be covered with enough money to spare for either band, and a minimum of $10 should be made. The conditions under which this set ticket price will fail are if less than about 200 people attend, because then, they simply would not be enough to cover the costs, because as the number of ticket buyers decreases, the necessary minimum price increases.

Activity 4

200<x<300When Band A performs, prices should be between $8.50 to $10, seeing as how when 200 people attend, the lowest ticket price should be $9.75, and when 300 people attend, the lowest ticket price should be $8.50, but only if Band A performs. If Band B performs, the prices should be between $8.92 to $10, seeing as how when 200 people attend, once again the price will be $9.75, but if 300 people attend, the price should be $8.92, but only if Band B performs.

When looking for the lowest price possible, even at the risk of not covering the costs, the tickets should cost $8.51, so that the costs are at least covered if 300 people attend and Band A performs, with a little bit of money made on the side.

y>9.75x

If the objective is to be able to cover the cost of the dinner dance when it’s at its greatest, the minimum ticket price should be $9.76, so that the costs are always covered, even if either band plays and only 200 people were to attend.

y<8.5x

x<300, x>200, y<8.5x, y>9.75x 300>x>200; 8.5x>y>9.75x