7.4 S KM & PP 1

7.4 Application Problems

7.4 S KM & PP 2

Word Problem Basics

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

7.4 S KM & PP 3

Tickets?

Tickets for the Sacramento Kings cost $90.00 for seats in the Lower Level and $70.00 for seats in the Upper Level. 25 students decide to attend a game. They spent $1910.00. How many of each ticket did they buy?

7.4 S KM & PP 4

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 5

• IDENTIFY your VARIABLES

Tickets?

• L = Number of tickets purchased in the

Lower Level

• U = Number of tickets purchased in the

Upper Level

7.4 S KM & PP 6

• Write a COMPLETE SYSTEM

Tickets?

1910U70L90

25UL

7.4 S KM & PP 7

• Write a COMPLETE SYSTEM

Tickets?

$ Tickets $•Tickets

Lower 90 L 90L

Upper 70 U 70U

25 1910

7.4 S KM & PP 8

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 9

Tickets

1910U70L90

25UL

7.4 S KM & PP 10

1910U70L90

25UL

Tickets?

1910U70L90

1750U70L70

160L20

70

20160

L

8L

7.4 S KM & PP 11

1910U70L90

25UL

Tickets?

8L 25U8

17U

7.4 S KM & PP 12

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 13

Tickets?

Tickets for the Sacramento Kings cost $90.00 for seats in the Lower Level and $70.00 for seats in the Upper Level. 25 students decide to attend a game. They spent $1910.00. How many of each ticket did they buy?

The students bought 8 Lower

Level tickets and 17 Upper Level

tickets

7.4 S KM & PP 14

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 15

Grain Mixture

Mrs. Peterson’s horse Red Rider needs 25 pounds of food, with an average of 9% protein, a day. Alfalfa contains 8% protein, while rolled oats contain 12% protein. How many pounds a day of alfalfa and rolled oats should she use?

7.4 S KM & PP 16

• IDENTIFY your VARIABLES

Grain Mixture

• A = Number of pounds of alfalfa fed

each day.

• R = Number of pounds of rolled oats

fed each day.

7.4 S KM & PP 17

Write a COMPLETE

SYSTEM

)25(09.0R12.0A08.0

25RA

7.4 S KM & PP 18

• Write a COMPLETE SYSTEM

Grain?

% Pounds %•Pounds

Alfalfa 0.08 A 0.08A

Upper 0.12 R 0.12R

0.09 25 0.09(25)

7.4 S KM & PP 19

Write a COMPLETE

SYSTEM

)25(09.0R12.0A08.0

25RA

R25A

25.2R12.0)R25(08.0 25.2R12.0R08.02

25.2R04.02

7.4 S KM & PP 20

Solve for R

)25(09.0R12.0A08.0

25RA

25.2R04.02

25.0R04.0 25.0R04.0

04.025.0

R

25.6R

7.4 S KM & PP 21

Solve for A

)25(09.0R12.0A08.0

25RA

2525.6A

25.6R

75.18A

7.4 S KM & PP 22

Clearly Answerthe Question

in Words.

Mrs. Peterson’s horse Red Rider needs 25 pounds of food, with an average of 9% protein, a day. Alfalfa contains 8% protein, while rolled oats contain 12% protein. How many pounds a day of alfalfa and rolled oats should she use?

She should feed 6.25 pounds of rolled oats and 18.75

pounds of alfalfa a day.

7.4 S KM & PP 23

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 24

Check! Check!

1353

134

yx

yx

),( 54

4(4) 3( 5) 1

3(4) 5( 5) 13

7.4 S KM & PP 25

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 26

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 27

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 28

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 29

• IDENTIFY your VARIABLES

• Write a COMPLETE SYSTEM

• Algebraically SOLVE the SYSTEM

• CLEARLY ANSWER the question(s) in WORDS

• REALITY CHECK ? Does your answer make sense?

Word Problem Basics

7.4 S KM & PP 30

Try this one again?

A piggy bank contains twenty-four nickels and quarters. The coins have a total value of $3.20. Determine the number of nickels and the number of quarters in the bank ?

2032505

24

.Q.N.

QN

7.4 S KM & PP 31

How about this one?

20282822

120

.E.C.

EC

A postal clerk sold some 22 cent and some 28 cent stamps. Altogether he sold 120 stamps for a total cost of $28.20. How many of each type stamp were sold? LET C = # of 22 cent stamps E = # 28 cent stamps

7.4 S KM & PP 32

How about this one?

20282822

120

.E.C.

EC

A postal clerk sold some 22 cent and some 28 cent stamps. Altogether he sold 120 stamps for a total cost of $28.20. How many of each type stamp were sold? LET C = # of 22 cent stamps E = # 28 cent stamps

7.4 S KM & PP 33

Pairs of Angles!

7.4 S KM & PP 34

Pairs of Angles!

7.4 S KM & PP 35

C Complements

90 yx

xy

7.4 S KM & PP 36

S Supplements

180 yx

x y

7.4 S KM & PP 37

Angles not Angels!

Two angles are complementary. The larger angle is 9o more than eight times the measure of the smaller angle. Find the measures of the two angles.

LS

9)(8

90

SL

SL

7.4 S KM & PP 38

Angles not Angels!

9)S(8L

90SL

8( S) 9 S 90

9( S) 9 90

9( S) 81

7.4 S KM & PP 39

Angles not Angels!

9)(8

90

SL

SL

81S

9

S 9

7.4 S KM & PP 40

Angles not Angels!

90SL

9)(8

90

SL

SL

S 9 909L

81L

9Sand81L

7.4 S KM & PP 41

Angles not Angels!

9o and 81o

9)(8

90

SL

SL

8( S) 9 S 90 9( S) 9 90

9( S) 81 81

S9

S 9

7.4 S KM & PP 42

Try this one!

A piggy bank contains twenty-four nickels and quarters. The coins have a total value of $3.20. Determine the number of nickels and the number of quarters in the bank ?

2032505

24

.Q.N.

QN

7.4 S KM & PP 43

That’s All Folks!