Unit Activity Essays (1253 words) - Mathematics,

Unit Activity Unit: Systems of Equations This activity will help you meet these educational goals: Mathematical Practices-You will make sense of problems and solve them, reason abstractly and quantitatively, use mathematics to model real-world situations, and look for and express regularity in repeated reasoning. Introduction In this unit, you used different methods to create and solve linear equations. You modeled scenarios using linear inequalities and solved them with the help of graphs. You studied patterns and sequences and were introduced to function notation, range and domain of functions, and different ways of representing a function. In this activity, you will analyze real-world situations by modeling them as linear equations or inequalities. __________________________________________________________________________ Directions and Analysis Task 1: Self-Publishing You've written your first novel and, like many first-time authors, can't find a publisher. So you've decided to self-publish your book. You need to work out the cost of printing the book. a. If the cost of printing the novel includes a base cost of $1,550 plus $4 per book, write a function that represents the cost of printing x copies of the book. Type your response here: b. If you want to cover the printing costs by printing and selling only 50 copies of the book, at what price must you sell the book? Type your response here: c. Based on the book price per copy you calculated in the previous task, write a function to represent your income if you sell x copies. Type your response here: d. After spending $200 on market research, you discover that you can sell many more copies of your book if you price it at $20. Write new functions for both your expenses and your income from selling x copies. Type your response here: e. Use the Edmentum Graphing Tool to graph the two functions you wrote in part d. Examine the graph, and estimate the minimum number of copies of your book you must print and sell to avoid losing money. Capture a screenshot of your graph, and include it with your answer. Type your response here: f. Solve the system of equations you derived in part d to find the exact number of copies (rounded up to the nearest whole number) you need to sell to avoid losing money. Type your response here: Task 2: School Fundraising Your school is planning a fundraising dinner. The expense for this event must not exceed $2,475.00. The team organizing the event has calculated that the cost per adult guest will be $18.00 and the cost per child guest will be $9.00. The venue can hold no more than 150 guests. a. Write a system of inequalities that represents this situation. Type your response here: b. Use the Edmentum Graphing Tool to graph the system of inequalities you created in part a. Highlight the region under each inequality using a different color. Then highlight the region common to both inequalities using a pattern such as horizontal, vertical, or diagonal lines. Capture a screenshot of your graph, and paste it in the space provided. Paste your graph here: c. Using the graph, determine the maximum number of adults (rounded up to the nearest whole) who could can attend the dinner and fill the venue to capacity. Type your response here: d. If the event were held in a venue that can accommodate 200 guests, what is the maximum number of adults who could attend if the event fills the venue to capacity? Include a screenshot of your revised graph with your answer. Type your response here: e. If you want to find a venue with a capacity that guarantees you cannot go over budget, what is the maximum number of people the venue will hold? Type your response here: f. The school aims to raise a minimum of $5,250 after paying for all the expenses. If the school collects $50 per guest and chooses a venue that can seat not more than 150 guests, what is the minimum number of children that must attend the event? Include a screenshot of your graph with your response. Type your response here: Task 3: Ancestry of a Male Honeybee Honeybee reproduction is an interesting phenomenon. When a queen bee lays an egg, the egg does not need to be fertilized by a male honeybee to hatch. The egg will develop into a male or a female honeybee depending on whether the egg is fertilized by a male honeybee. The outcome is determined