Winter Wonderland Holiday Party
Food ~ I believe that we should use Pizza Palace because more money would be saved by purchasing pizza rather than burgers or sandwiches. With purchasing 1/5 of the seventh grades pizza the school would save ninety dollars on burgers and thirty dollars on sandwiches. When purchasing for 2/5, or more of the seventh grade, hundreds of dollars would be saved by purchasing pizza rather than burgers or sandwiches.
Music ~ I believe that wee should use Classic Spin because more money would be saved by using Classic Spin rather than Spin City. Starting out with a 2 hour party, 5 dollars will be saved. Increasing the time by only half an hour, the school saves 25 dollars. For every half an hour added to the party following a 2.5 hour party, the money saved increases by 20 dollars.
To solve this equation, I first found the constant range for each catering business. I plugged in my estimate for the number of people that would attend the party and multiplied the estimate by the constant rate of change. I made sure to include the addition fee, or y-intercept by adding it to the equation. There will never be a number of students where the companies will cost the same. As the number of students increases so does the cost. I found this by plugging in numbers for x in each equation and comparing the solutions of each company to one another. These steps I used to solve whether or not there will be a number of students where both companies will cost the same simply relate to order of operations. Order or operations, parentheses, exponents, multiplication, division, addition, and subtraction, are used when solving equations. When I plugged in numbers to find whether the costs could ever be the same, I used these steps to find a solution in the order they are shown. If the budget for food was limited to 1000 dollars only a total of 118 seventh graders would be able to attend the party. A decimal or fraction could not be part of this problem because you cannot have only a faction of a person attend a party.
To solve this equation, I first found the constant rate of change for each music business . I used my different amounts of times for the party and multiplied that by the constant rate of change. I made sure to include the additional fee, or y-intercept by adding it to the equation. There will never be a number of hours where both companies will cost the same. As the number of hours increases, so does the total cost. To find this I first simplified the 2 equations by combining like terms. I replaced the x's in the equation with one and then solved. I compared the solution of each equation and the numbers were not equivalent. The steps I used to find whether or not there could ever be a number of hours where the 2 companies could cost the same easily compare to order of operations. Like order of operations, I first solved for what was inside the parentheses. There were no exponents so I continued on to multiplication and division. I multiplied numbers on both sides of the equation and then added y-intercepts. If a limit of 1000 dollars was placed on music, 10 hours and 45 minutes of music could be provided. In this situation a decimal or fraction can be used because hours can be simplified to minutes and minutes to seconds.