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[Chapter 1 & 2][Tree diagram for counting combinations]
[Chapter 3 & 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]

 

Answers to Homework Problems

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

 

3.         FOLLOW THE BOUNCING BALL

            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

ABDC       BADC        CADB       DACB

ACBD       BCAD        CBAD       DBAC

ACDB       BCDA        CBDA       DBCA

ADBC       BDAC        CDAB       DCAB

ADCB       BDCA        CDBA       DCBA

 

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 Set A

 

 

3.    EGGS IN A BASKET

 

119

 

4.    DARTBOARD

 

23, 58, 31, 6, 15

 

5.    FIND THE NUMBER

 

                      Answer: abcd is 2178

6.    a. GIRLS + GIRLS = SILLY
 

Two possible answers: 

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;
       Adele Higgins, Jazz;
       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 Set A

 

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

Add the next even number.

 

     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

Add the two previous terms and then add 1.

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

 

      Answers will vary

 

 

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 Set A

 

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 Set A

 

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?    )

 

5.   SHADED AREA

        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?
                  (express your answer in terms of x)
         c. How big is the gas tank?
                  (express your answer in terms of x)
         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.  1371.5 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

 

7.   READING RATE (PART I)

 

       0.44  pg/mm

 

8.  READING RATE (PART II)

 

       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 Set A

 

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

                         ch10-12                                  

 

12.    MAGIC SQUARES

                       ch10-13            

                        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

                     ch10-14A           ch10-14B                 

          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.

 

 

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