1. L ESSON 2.12 U SING S YSTEMS OF E QUATIONS IN THE R EAL W ORLD Concept: Represent and Solve Systems EQ: How are systems of equations used in the real world? (Standards REI.5-6,10- 11) Vocabulary : System of Equations, Event

2. S TEPS TO WRITING A SYSTEM OF EQUATIONS OR INEQUALITIES FROM A WORD PROBLEM 1. Read the problem. 2. Make a table or a list of what you know. 3. Identify the two unknown quantities and define each of them with a variable. 4. Exam your table or list to identify what two events are being compared. 5. Write two equations (one per event ) relating the known information to the two variables. 6. Solve the system. 7. Interpret and apply your solution to the context of the problem.

3. B OOMERANGS http://www.youtube.com/watch?v=zl10s5xe2-4

4. G UIDED P RACTICE – E XAMPLE 1 Phil and Cathy plan to make and sell boomerangs for a school event. The money they raise will go to charity. They plan to make them in two sizes: small and large. Phil will carve them from wood. The small boomerang takes 2 hours to carve, while the large one takes 3 hours to carve. Phil has a total of 24 hours available for carving. Cathy will decorate them. She only has time to decorate 10 boomerangs of either size. Write and solve a system of equations to determine how many small and large boomerangs they should make?

5. Two size boomerangs: small and large Small boomerang takes 2 hours to carve Large boomerang takes 3 hours to carve Phil has a total of 24 hours to carve Cathy only has time to decorate 10 boomerangs of either size. # of small boomerangs to make # of large boomerangs to make S = # of small boomerangs to make L = # of large boomerangs to make Carving Decorating

6. G UIDED P RACTICE – E XAMPLE 1, CONTINUED Solve the system of equations using the substitution or elimination method.

7. Two size boomerangs: small and large Small boomerang takes 2 hours to carve Large boomerang takes 3 hours to carve Phil has a total of 24 hours to carve Cathy only has time to decorate 10 boomerangs of either size. # of small boomerangs to make # of large boomerangs to make S = # of small boomerangs to make L = # of large boomerangs to make Carving Decorating

8. P ARTNER P RACTICE – E XAMPLE 2 Movie tickets are $9.00 for adults and $5.00 for children. One evening, the theater sold 45 tickets worth $273.00. Write and solve a system of equations to determine how many adult tickets were sold and how many children’s tickets were sold.

10. P ARTNER P RACTICE – E XAMPLE 3 Esther has a total of 23 dimes and pennies. The value of her coins is $1.85. Write and solve a system of equations to determine how many dimes and how many pennies Esther has.