1. HW#6: Real-Life Examples Answers 1. a.) 10 t-shirts need to be ordered for both shops to charge an equal amount. b.) If 9 or less t-shirts are ordered, Shop A is less expensive. If 11 or more t-shirts are ordered, Shop B is less expensive 2.a.) C = 1.75 + 1.80m C = 2.50 + 1.20m b.) At 1.25 miles the companies charge the same amount. 3. C = #children A = #adults C + A = 2200 1.50C + 4.00A = 5050 1500 children and 700 adults attended.

2. Tues, 3/9/10 SWBAT… apply systems of equations Agenda 1. WU (10 min) 2. Review hw#5 3. Concept Summary – Solving Systems of Equations (15 min) 4. Real-life systems examples Warm-Up: 1. The table below shows the number of car’s at Santo’s Auto Repair Shop. Santos has allotted 1100 minutes for body work and 570 minutes for engine work. Write a system to determine the time for each service. HW#6-Real life examples and Practice Test

3. Auto Shop Questions Q: What does the first equation in the system of equations represent? A: The amount of time to perform body work repair for 3 cars and body work maintenance for 4 cars Q: What does the second equation in the system represent? A: The amount of time to perform engine repair for 2 cars and engine maintenance for 2 cars. Q: What will the solution to the system represent? A: The number of minutes allotted per repair and the number of minutes allotted per maintenance. Q: If you multiply the second equation by -2, what variable could you eliminate by adding the equations? A: The variable m.

4. Fill in the chart below: MethodThe Best Time to Use Graphing Substitution Elimination using Addition Elimination using Subtraction Elimination using Multiplication

5. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. To visualize the equations. Substitution Elimination using Addition Elimination using Subtraction Elimination using Multiplication

6. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. To visualize the equations. Substitution If one of the variables in either equation has a coefficient of 1. Elimination using Addition Elimination using Subtraction Elimination using Multiplication

7. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. To visualize the equations. Substitution If one of the variables in either equation has a coefficient of 1. Elimination using Addition If one of the variables has opposite coefficients. Elimination using Subtraction Elimination using Multiplication

8. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. To visualize the equations. Substitution If one of the variables in either equation has a coefficient of 1. Elimination using Addition If one of the variables has opposite coefficients. Elimination using Subtraction If one of the variables has the same coefficients. Elimination using Multiplication

9. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. To visualize the equations. Substitution If one of the variables in either equation has a coefficient of 1. Elimination using Addition If one of the variables has opposite coefficients. Elimination using Subtraction If one of the variables has the same coefficient. Elimination using Multiplication If none of the coefficients are 1 and neither of the variables can be eliminated by simply adding or subtracting the equations.

10. Which method is best to use? Why? 1.x = 12y – 14 3y + 2x = -2 Substitution; one equation is solved for x 2. 20x + 3y = 20 -20x + 5y = 60 Elimination using addition to eliminate x 3.y = x + 2 y = -2x + 3 Substitution; both equations are solved for y

11. 4. -20x + 3y = 20 -20x + 5y = 60 Elimination using subtraction to eliminate x 5. -5x – 3y = 20 -5x + 3y = 60 Elimination using subtraction to eliminate x OR elimination using addition to eliminate y 6.3x + 3y = 9 4x + 2y = 8 Elimination using multiplication

12. Ex. 1a: Elimination using Multiplication (eliminate the x variables) 5x + 6y = -8 2x + 3y = -5

13. Ex. 1b: Elimination using Multiplication (easiest to eliminate the y variables) 5x + 6y = -8 2x + 3y = -5

14. Ex 3b: Elimination using Multiplication (Eliminate the y variables) 3x + 3y = 9 4x + 2y = 8 Answer: (1, 2)

15. How a fair manager uses systems of equations to plan his inventory The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. How many children and how many adults attended? HW#6, Problem #3

16. How a customer uses systems of equations to see what he paid Two groups of students order burritos and tacos at Los Gallos. One order of 3 burritos and 4 tacos costs $11.33. The other order of 9 burritos and 5 tacos costs $23.56. How much did each taco and burrito cost?

17. How a school uses systems of equations to see how many tickets they sell Your class sells a total of 64 tickets to the school play. A student ticket costs $1 and an adult ticket costs $2.50. Your class collects $109 in total tickets sales. How many adult and student tickets did you sell?

18. How a customer uses systems of equations to see what he paid A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?

19. How a bakery uses systems of equations to track their inventory La Guadalupana Bakery sells pies for $6.99 and cakes for $10.99. The total number of pies and cakes sold on a busy Friday was 36. If the amount collected for all the pies that day was $331.64, how many of each type were sold?

20. How a math student uses systems of equations to solve math puzzles! The sum of two numbers is 25 and their difference is 7. Find the numbers.

21. How a math student uses systems of equations to solve math puzzles! Twice one number added to another is 18. Four times the first number minus the other number is 12. Find the numbers.

22. How a customer uses a system of equations to see what he paid Two groups of friends go to Los Gallos. The first group orders five tacos and four burritos, and they spend a total of $22.50. The second group orders eight tacos and three burritos, and they spend a total of $23.25. How much does each taco and each burrito cost? (There is no tax ) HW, Problem #1

23. How a movie manager uses a system of equations to plan his profit A movie theater can hold a total of 300 people. The theater has sold-out for the opening night of The Hunger Games movie. Each adult ticket costs $10, and each student ticket costs $8. If the theater made $2,582, how many of each type of ticket did they sell? HW, Problem #2

24. If you would like additional practice to prepare for Monday’s system of equations test, on the Infinity website, you will find: 1. System of equations study guide (15 problems) 2. PPT – System practice (12 problems)