**Linear Equations Performance Task**

Introduction

Bands

Caterers

Decorations

We recently held a fundraiser and raised $150 to purchase balloons and streamers from Party City.

Balloons cost 0.40 each

Packages of streamers cost $1.25 each.

We wanted everyone to have a balloon tied to their chair.

To find the price of balloons, we have to multiply .4 by 200, which equals 80. This means that we can buy 80 dollars worth of balloons. For 300 people, you multiply .4 by 300 to get 120.

From there, we subtract 150 by 80 to get 70. We have $70 to spend on streamers for 200 people. For 300 people, we subtract 150 by 120 to get 30.

Then, we divide 70 by $1.25 to get 56. For 300 people, we divide 30 by 1.25 to get 24.

Formulas:

Solution

Overall, we used many equations such as linear equations and standard form. By using those formulas, we have found an easier way to find the total amount of money and how much an item costs. Plus, the ticket price would be $14.75, using the y= mx + b format. At the end, we hoped that the hard work that we had put in preparing the dance would involve with many students coming and enjoying the night.

For this year's 8th grade dinner-dance, the 8th Grade Student Activities Committees have been working on planning the band, caterer, and decorations. To persuade students to come to the event we had to minimize our expenses. Our specific goal is 300 students to attend ,but in another case, we have to be prepared if only 200 students are coming. To make this dance a successful party, we have included data that consists of mathematical calculations and reasoning for the essentials things we need for the party. Last but not least, we have determined the amount of ticket price we should charge for both situations.

**By Alaina, Christine, Eurah, and Gabby**

~Stud Muffins~

y=1.25x+250

~Cray-Z Hearts~

y=600

Villagio's: 11.85 per person and a fee for set up and delivery. Charged $2,303 at their last function.

Brown Stone: Charged 1,897.50 for 150 people and at a function with 328 people charged $4,078.

Find the fee for set up and delivery at Villagio's.

For the Caterers section, there are two choices that we decided with. The choices are theBrown Stone and Villaggio's but there were many restrictions for the cost of each category.

Find the difference between both events were once planned before.

328-150=178

4,078-1897.50=2,180.5

Divide

2180.5/178

Write

y=12.25x+b

Rewrite so that you can solve for both variables

y-1897.5=12.25(x-150)

Solve

y-1897.5=12.25x-1837.5

+189.5 +189.5

Answer

y=12.25x-6

~300 people~

150=1.25x+80

~200 people~

150=1.25x+120

Cupcake time!

made by Gabby!!

The band, Cray-Z hearts charges $600 and the band, Stud Muffins charges $250 plus 1.25 per student attending.

For 200 students, we use the equation y=1.25(200)+250 for the Stud Muffins. 1.25x200=250 and when we add that to 250 to get $500.

For 200 people, Stud Muffins costs less money.

For 300 students, we use the equation y=1.25(300)+250. 1.25x300=375 and when we add that to 250, we get $625.

For 300 people, Cray-Z Hearts costs less.

Formulas:

y=12.25(300)

y=12.25(200)

Ticket Prices

~300 people~

$14.25 per person in order to break even for $4,275

~200 people~

$14.75 per person to break even for $2,950

To get our answers we had to add all the money spent on the dance (not including decorations, which were already paid for by the students). Then we had to divide that amount of money by how many people were attending the dance (300 or 200)