Section 5.1.4 How Can I Use Systems

#5-44 How Tall is Harold Dinah and Jamal were eating as they came into Algebra 4 class from lunch. Someone had left a book on the floor and they tripped. As they each hit the floor, the food they were carrying went flying across the room directly toward Harold who was showing off his latest dance moves.

#5-44 How Tall is Harold As Jamal and Dinah watched in horror, Jamal’s cupcake and Dinah’s sandwich splattered Harold right on top of his head! Jamal’s cupcake flew on a path that would have landed on the floor 20 feet away from him if it had not hit Harold. Dinah’s sandwich flew on a path that would have landed on the floor 24 feet away from her if it had not hit Harold. Jamal’s cupcake got up 9 feet high, and Jamal’s sandwich reached a height of 6 feet before hitting Harold.

#5-44 How Tall is Harold How tall is Harold? Show solution in as many ways as possible.

Generate tables of values one for each person x y 10 9 20 x y 12 6 24 Now run the Quadratic Regression (choice 5) on your calculator; remember to store one equation in Y1 and the other in Y2

Adjust the window of your calculator Once you know each formula and you have stored them in Y1 and Y2, use intersect key to find the point of intersection. What does x coordinate of POI represent? What does y coordinate of POI represent? Once you know each equation, use the EQV method to find x and y.

Click of the grid and turn on each function/point series.

#5-45 Your math class wants to collect money for a field trip, so it decides to sell two kinds of candy bags. The Chocolate Lovers bag costs 4.25 for five chocolate truffles and two caramel turtle candies. The Combusting Caramel Bag costs 3.50 for eight caramel turtle candies and two chocolate truffles. How much does each chocolate truffle and caramel turtle candy cost?

solution Let x be the cost of Truffles Let y be the cost of Caramel Turtles Then for each type of bag write an equation: 5𝑥+2𝑦=4.25 2𝑥+8𝑦=3.5

Solution There are several methods to solve the systems of equations you just wrote. The following is only one way: 5𝑥+2𝑦=4.25 Multiply by -2 2𝑥+8𝑦=3.5 Multiply by 5

solution −10𝑥−4𝑦=−8.5 10𝑥+40𝑦=17.5 Now combine. 36y=9 y=0.25 Sub in one of the original equations. 5𝑥+2(0.25)=4.25 x=0.75

X=0.75 and y=0.25 Now that you know the price of each kind of candy, check your work by substituting your answer into the second equation: 2(0.75)+8(0.25) ? 3.5 1.5+2 = 3.5

#5-46 Jobs Lucky you! You are a new college graduate and have already been offered two jobs. Each job involves exactly the same tasks, but the salary plans differ, as shown below. Job A offers a starting salary of 52,000 per year with an annual increase of 3,000. Job B starts at 36,000 per year with a raise of 11% per year.

#5-46 Jobs A. Under what conditions would Job A be a better choice? When would Job B be a better choice? Use graphs, tables and equations to help you justify your answer.

Solution Let x be the number of years. JOB A: 𝑦=52,000+3000𝑥 JOB B: 𝑦=36,000 (1.11) 𝑥 Graph each… make sure to display the window you choose.

graph

solution By using the intersect key: POI=( 6.625, 71876.17) What does x coordinate of POI represent? What does y coordinate of POI represent? So up to 6 years Job A is a better option. Starting with year 7 Job B is a better option.

graph

#5-46 Jobs B. How would you change this problem slightly so that Job B is always a better choice? How could you change it so that Job A is always better.? If it is not possible for Job A or Job B to always be the better choice, explain why not.

On your own: Review your notes. Rewrite and fortify them if needed. Update your vocab list, if needed. Review and Preview Page 234 # 48-53