LESSON 2.12USING SYSTEMS OF

EQUATIONS IN THE REAL WORLD

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

STEPS 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.

BOOMERANGShttp://www.youtube.com/watch?v=zl10s5xe2-4

GUIDED PRACTICE – EXAMPLE 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?

• 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 makeL = # of large boomerangs to make

• Carving• Decorating

GUIDED PRACTICE – EXAMPLE 1, CONTINUEDSolve the system of equations using the substitution or elimination method.

Substitution MethodSolve the second equation for s.

Substitute this new equation intoThe first one.

Substitute this value into the amendedEquation from step 1.

• 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 makeL = # of large boomerangs to make

• Carving• Decorating

They should make 4 large and 6 small boomerangs.

PARTNER PRACTICE – EXAMPLE 2Movie 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.

PARTNER PRACTICE – EXAMPLE 3Esther 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.