Math 120
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# Homework

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[Chapter 1 & 2][Tree diagram for counting combinations]
[Chapter 3]
[Chapter 4]
[Matrix logic table 1][Matrix logic table 2]
[Chapter 5 & 6]
[Chapter 7 & 8]
[Chapter 9][graph paper]                             Scroll Down for HW Answers!
[Chapter 10]         [folding box]
[Chapter 11]
[Chapter 12]

Warning: You should only use these answers to check the correctness of your work
and you need to show all steps for any credit.

## Chapter I, Problem Set A

1.         WORM JOURNEY

10 days

2.         THE UPS AND DOWNS OF SHOPPING

13 floors

460 feet

4.         FLOOR TILES

320 tiles

5.         COUNTING ON NINJA TURTLES

22 turtles

7.         RACE

Ursula, Alma (3 m behind), Cathy (3 m behind), Lani (2 m behind), Isabel (2 m behind), and Betty (2 m behind)

8.      A WHOLE LOTTA SHAKIN' GOIN' ON!

15 handshakes

## Chapter 2, Problem Set A

1.    CARDS AND COMICS

Cards @ \$1.20                Comics @ \$.60

5                                        0
4                                        2
3                                        4

2                                        6

1                                        8
0                                       10

2.    FREE CONCERT TICKETS

A = Alexis, etc.

ABCD       BACD        CABD       DABC

ACDB       BCDA        CBDA       DBCA

3.    IT SURE IS TOUGH TO GET AN APARTMENT THESE DAYS

In the ninth month Plan A costs more (\$640 per month vs. \$620 per month for Plan B). But for the whole year plan B costs more (\$6990 total vs. \$6780 for Plan A).

4.       STORAGE SHEDS

8 ft x 8 ft           10 ft x 10 ft            12ft x l2ft        15 ft x 15 ft

8 ft x 10 ft         10 ft x 12 ft            12ft x 15 ft

8 ft x 12 ft         10 ft x 15 ft

8 ft x 15 ft

5.    MAKING CHANGE

10 ways

7.      KYLE CRAVES CANDY

There are 10 ways

Five        Ten      Fifteen              Total

8             0              0                       40

6             1              0                       40

5             0              1                       40

4             2              0                       40

3             1              1                       40

2             3              0                       40

2             0              2                       40

1             2              1                       40

0             4              0                       40

0             1              2                       40

# Chapter 3, Problem SetA

119

4.    DARTBOARD

23, 58, 31, 6, 15

5.    FIND THE NUMBER

6.    a. GIRLS + GIRLS = SILLY

G = 3, I = 0, L = 9, R = 4, S = 6, Y = 2  OR

G = 1, I = 9, L = 0, R = 5, S = 3, Y = 6

b. GOOD + DOG = FANGS

A = 0, D = 8, F = 1, G = 9, N = 2, 0 = 4, S = 7

7.    SEND + MORE = MONEY

9567 + 1085 = 10652

8.    THE THREE SQUARES

Chris is 19, Phyllis is 23, Bob is 28.

9.    KNIGHTS AND KNAVES

There is only one knight.

# Chapter 3, Problem Set B

1.   THE SIDEWALK AROUND THE GARDEN

172 feet

2.   A NUMBER OF OPTIONS

24 ways

3.   GOOD DIRECTIONS?

Go 2 blocks east and one block south. (two more possible answers)

4.   HIGH SCORERS

Heather:  25; Sara: 23; Martina: 19; Donna: 17; Kellene: 11

5.   WAYS TO SCORE

14 ways

# Chapter 4, Problem Set A

1.   SCHEDULES

a.   Jill's schedule                                      b.     Tom's schedule

1    Band                                                    I             PE

2    PE                                                       2           Math

3    Science                                                3            Drama

4    Math                                                   4            Science

5    Lunch                                                  5            Lunch

6    English                                                6            English

7    History                                                7            Typing

c.             Leanne's schedule is impossible as she has to take both Math and PE during
second period and has no class to take during seventh period.

d.             Mea's schedule has many possibilities.

e.             Part I: Jose's first schedule looks like this

1            PE

2            Math

3            Drama

4            Science

5            Lunch

6            English

7            History

Part 2:     Because first period PE is closed, there is no way for Jose's schedule to work. He won't be able to take Drama because he will have to take Science third period to make his schedule work. So he must pick another elective, either Band or Typing.

Part 3: Now with the new sixth period science class, Jose's schedule will work.

1         English

2         Math                 (Note: Math and PE can be switched.)

3         Drama

4         Lunch

5         PL

6         Science

7         History

2.   THE FISHING TRIP

Sally first, Larry second, Woody third, Marta fourth

3.   CABINET MEMBERS

Georgianne, President;
Norma, Vice President;
Inez, secretary of state;
Paula, secretary of education;
Colleen, secretary of treasury

5.   MUSIC PREFERENCES

Jack Mullin, country western;
Mike Hardaway, rock;
Edna Richmond, classical

6.   SUSPECTS

Connie Wilde, purple hair:
Morgan Theeves, scar;

Dana, tall and blonde;
Cary Fleece, birthmark

# Chapter 4, Problem Set B

1.   PHONE NUMBER

492-2804

3.   SPORTING EVENTS

Ed, baseball, Monday

Judy frisbee, Tuesday

Mama, golf Thursday

Lisa, soccer, Friday

4.   THE BILLBOARD

7 lines

# Chapter 5, Problem SetA

1.   SEQUENCE PATTERNS

a.   2, 5, 10, 17, 26, 37, 50

Add next odd number. Or, each term is 1 more than a perfect square.

b.     64, 32, 16, 8, 4, 2, 1, 1/2

Divide by 2. Or, each term is a descending power of 2.

c.     5, 10, 9, 18, 17, 34, 33, 66, 65, 130

Multiply by 2 and then subtract 1.

d.        1, 3, 7, 13, 21, 31, 43, 57

e.        2, 3, 5, 9, 17, 33, 65

Add the next power of 2. Or, 2, 3, 5, 9, 16, 27, 43. The difference of the differences increases by 1. There are probably other answers.

f          1, 5, 13, 26, 45, 71, 105, 148, 201

Starting with 4, the difference of the differences increases by 1.

g.        1, 2, 6, 24, 120, 720, 5040, 40320, 362880

Multiply by the next higher number. Or, each term is just n! (n factorial).

h.        1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177

2.   AIR SHOW

400

The pattern is the square of the number of rows.

3.   RECTANGULAR DOTS

34 x 35 = 1190

4.   PENTAGONAL NUMBERS

425

Add together a triangular number and a square number. The triangular number has one fewer dots per side than the square number.

5.   LAST DIGIT

257 ends in 2. The pattern goes 2,4,8,6,

8.   BEES

231

This is a Fibonacci sequence added up.

9.   PASCAL'S TRIANGLE

1, 6, 15, 20, 15, 6, 1

1, 7, 21, 35, 35, 21, 7, 1

1, 8, 28, 56, 70, 56, 28, 8, 1

1, 9, 36, 84, 126, 126, 84, 36, 9, 1

10.   OTHER PATTERNS IN PASCAL'S TRIANGLE

# Chapter 5, Problem Set B

1.   GOLF MATCH

Diana will tee off second.

2.   MACARONI AND CHEESE

1/3 of a pound.

3.   COMIC OF THE MONTH

\$22.42

5.   ROO AND TIGGER

Roo by 4 feet.

# Chapter 6, Problem SetA

1.   DIMES AND QUARTERS

8 quarters, 13 dimes

2.   MARKDOWN

\$34.30

3.   TAX

\$14.49

6.   CHECKING ACCOUNT

39 checks

8.   BASEBALL CARDS

35 cards

9.   STAMPS

five 16-cent stamps and seven 7-cent stamps

10.   A BUNCH OF CHANGE

14 dimes, 25 nickels, 19 quarters

11.   Special numbers

Use guess and check.

12.   After the football game

15 people

13.   TRAVELING TO MOM'S HOUSE

28 miles

14.   RIDING A HORSE

3 miles per hour

15.   Shopping Surprises

\$3.00 per dozen.

# Chapter 6, Problem Set B

1.   Football Scores

14 ways (when order is important).

2.   Animals

Use guess and check technique. Hint: lots of rabbits.

5.   LARRY LONGWAY AGAIN

3, 3, and 8

6.   Cakes and Tea

7 people, 2 cakes, 3 (cups of ) tea.

# Chapter 7, Problem SetA

1.   COFFEE

6 ounces
(Suggested sub-questions:
a. How much does 1 lb of coffee cost?
b. How much does 1oz of coffee cost?
c. How many oz of coffee can \$1.11 buy?  )

2.   SHARING EXPENSES

Many answers are possible. Each person's share is \$8.l6. Leroy needs \$5.84; Max
needs 84
¢; Alex owes \$5. 16; Kulwinder owes \$1.16; Bobbi owes 36¢.

(Suggested sub-questions:
a. How much did they spend totally?
b. What is the fair share for each person?
c. Who over paid and by what amount?
d. Who under paid and by what amount?
e. Who should give money to whom and by what amount? )

3.   AIRPLANE SEAT

240 seats

(Suggested sub-questions:
a. How many percent of the passengers were women?
b. How many percent of the passengers were girls?
c. How many percent of the passengers were men?
d. How many passengers were on the plane?
e. How many seats are on the plane?                 )

4.   SIX SQUARES

42 feet
(Suggested sub-questions:
a. What is the area of each square?
b. What is the length of each side of each square?
c. What is the perimeter of the figure?    )

100 - 25 p or 21.46. Note: the ¼ circles are all supposed to be the same size.
(Suggested sub-questions:
a. What is the area of the square?
b. What is the radius of each quarter circle?
c. What is the area of all those quarter circles?
d. What is the area of the shaded part?           )

6.   SAVINGS PLAN

12%

7.   TEST AVERAGE

94%

8.   CAR TRIP

36 minutes

9.   TEST TRACK

8 hours
(Suggest sub-questions:
a. How many gallons of gas does the car use per hour during idling?
(answer: since we can't figure this out, we use the variable x.)
b. How many gallons if gas does the car use per hour at 60mph?
c. How big is the gas tank?
d. How many gallons of gas are still left in the tank after idling for 10 hours
(assuming starting from a full tank)?
e. How many more hours can it run at 60 mph with the remaining fuel?   )

10.   BOX

1620 in.3

# Chapter 8, Problem Set A

1.   UNIT CONVERSIONS

a.  114.8 ft                     b. 51.8m                         c. 241.4 km

d.  29.2 mi                      e.  121.9 cm                    f. 34.3 in.

g.  1371.6 mm                h. 14.3 m/sec                 i. 18.95

j.   16.9qrts

2.   CHRISTINA'S TRIP

a.  51.6 mi/hr                b. 29 mi/gal                   c. \$1.19/gal

d.  75.6 ft/sec                e. \$2.12/hr                     f.  0.12 qt/min

g.  3.5 cents/min            h. 4.1 cents/mi

i.      24.4mi/\$               j. 1.8 gal/hr

3.   ANOTHER LONG COMMUTE

a. 2.5 gal                        b. 1.75 hrs                      c. 73.3 ft/sec

d.  \$1.89/hr                    e. \$1.32/gal                    f \$1.10/pass

g.  3.77 cents/mi            h. 262.5 pass-mi

i.   105 pass-mi/gal        j. 1.3 cents/pass-mile

4.   RULE OF THUMB

88 ft/sec, 58.7 ft/sec, 73.3 ft/sec

The rule of thumb is to multiply by 1.5.

5.   PROJECTILE

a.  102.3 mi/hr               b. 164.6 km/hr

6.   PAINTING CHIPMUNKS

Alvin, \$24; Simon, \$19; Theodore, \$18

0.44  pg/mm

about 20 or 21 books (20.58)

9.   NURSING

8.4   cc/hr

# Chapter 8, Problem Set B

1.   WANT A SMOKE?

14 years, 212 days, 22 hours  (using 365 days/yr)

2.    SESAME STREET LIVE

17 adults, 13 junior, 90 children.

5.    VOLLEYBALL LEAGUE

Buckeyes beat Bombay Bicycle, lost to Sacto Magazine and Red Skeletons.

# Chapter 9, Problem SetA

1.   DIAGONALS

275 diagonals

2.   SUM OF ODDS

25 million

3.   TV TRUCK

504 TV sets

4.   POTATOES

approx 74 pounds of potatoes; 7 soldiers

5.   SO MANY TRIANGLES

84 triangles

6.   TWENTY-FIVE MAN ROSTER

12 infielders/outfielders, 6 starting pitchers, 4 relief pitchers, 3 catchers.

9.     FIFTY-TWO CARD PICKUP

252 - 1

# Chapter 9, Problem Set B

1.   COVERING THE GRID

30 tiles

2.   TUPPERWARE PARTIES

20,475 parties

4.   JOGGING AROUND A TRACK

every 40 seconds

# Chapter 10, Problem Set A-1

1.   THREE ADULTS AND TWO KIDS

13 trips, starting with the two kids going across

2.   THE DOG, THE GOOSE, AND THE CORN

There are two solutions, which are virtually identical:

He must take the goose across first, leave it, and go back for the corn He then takes the goose back to the first side, leaving it and taking the dog across. He leaves the dog with the corn and returns across the river to retrieve the goose.

He must take the goose across first, leave it, and go back for the dog. He then takes the goose back to the first side, leaving it and taking the corn across. He leaves the corn with the dog and returns across the river to retrieve the goose.

5.   THE HOTEL BILL

The bellhop has \$2 that the women had paid. The hotel has \$55 from the women, and the bellhop has \$2. The women each paid \$19, and out of that total the bellhop has \$2 and the hotel has \$55. There is no missing dollar.
Franklin's argument is wrong because the \$57 includes the \$2 tip, he should subtract \$2 from \$57 instead of adding.

7.   WORCHESTERSHIRE PALACE

a.     16 moves                 b. 6 moves

# Chapter 10, Problem Set A-2

9.   JACK-QUEEN-DIAMOND

Jack of Diamonds, Queen of Diamonds, and Queen of Hearts

10.   BASEBALL SEATING

Aisle, Mom, Alyse, Dad, Kevin, Jeremy (or put Mom on the other side of the aisle)

11.    MAGIC TRIANGLE

12.    MAGIC SQUARES

There are actually a number of possible solutions. Some of  the others can be found by switching columns with columns or rows with rows.

13.    TRUE EQUATIONS

Switching the 4 and 8 with the 3 and 6 respectively yields another solution.

15.   CUBIST

E, right side up in normal orientation (Note: I appears twice.)

# Chapter 11, Problem Set A

1.   LOSING STREAK

\$9200

2.   GENEROSITY

\$252

4.   THE MALL

She started with \$124. She spent \$18 on a CD, \$53 on a dress, \$11 for lunch, \$14 on a book, \$12 for gas, and \$4 on a nail polish. She gave her sibling \$2.

6.   HOCKEY CARDS

Jack 25, Jill 15

7.   DONUTS

19 donuts

# Chapter 12, Problem Set A

1.   SENIOR CLASS

45 students

2.   HAMBURGERS AND HOT DOGS

45 like neither.

4.    EATING VEGETABLES

1, 4, 4, 0, 6

5.   THE FIELD TRIPS

88 children

6.   FAMILY

5 cousins were neither nieces nor aunts.

8.   BLOOD LINES

76, 12, 4, 24

10.   BOTTLE CAPS

25 cola, 45 orange, 55 root beer; 125 total

# Chapter 12, Problem Set B

4.   THE HOLIDAY PARTY

30 cousins that weren't nephews or uncles, 10 uncles that were cousins but not nephews

6.   EAST PARKING LOT

18 white vehicles.

A Member of the Grossmont-Cuyamaca Community College District