Grade Five Answers

Answer:

     1)  9+8+7+65+4+3+2+1 = 99   -> 7 addition signs.

     2)  9+8+7+6+5+43+21 = 99    -> 6 addition signs.

Answer:

 26+26+26 = 78

Answer:

     30 seconds * 4 * 197299 = 23675880 seconds.

Answer:

     The quickest way is to move each disk onto the first post
     except for the last disk -> which is 9 moves.

     Then move the last disk to the second post which is one
     move.  

     Then move each of the disks on the first post to the second
     post which is an additional 9 moves.

               9 + 9 + 1 = 19 moves

Answer:

     9 hours - (15 + 20 + 35)
     9 hours - 70 minutes
     7 hours + 120 minutes - 70 minutes = 7 hours and 50 minutes = 7:50 AM

Answer:

Answer:

     +1572          1753
     +1753          -152
     +1601         ------
     ------         1601
      4926

Answer:

                    1994      1996

     Eilosa         129       204
     Vertu          308       292
     Pridi           90        50
     Dedrun         500       600
     Antran         700       693
     Maran         1200      1500
                  -----------------
                   2927      3339

    3339 - 2927 = 412 therefore the population in '96 is greater

10)

Answer:

             ESTIMATE       ACTUAL
               320            315
               220            216
              3630           3629
             ------         ------
              4170           4160

11)

Answer:

Mass of Stone Henge + 95t = Mass of Leaning Tower
Mass of Leaning Tower + 557t = Mass of Great Pyramid

Therefore the mass of the Great Pyramid  = 2(2695t + 95t + 557t) = 6694t

12)

Answer:

     17 edges       9 faces        10 vertices

     Pentagonal Prism contains a  rectangular prism and a right
     trianglular prism.

13)

Answer:

        4 edges, 4 vertices and one 
        face come from square base.

          12E                8E
           8V                5V
           6F                5F

14)

Answer: There are many solutions. Here we have one solution.

              4V
              6E
              4F

15)

Answer:

        2³ = 8

16)

Answer:

    1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10  = 10 triangles
    1,2 / 2,3 / 6,4 / 4,1 / 10,7 / 7,6 / 9,8 / 8,10 / 9,5 / 5,3 = 10 triangles
    7,0,5 / 4,0,8 / 2,0,7 / 5,0,4 / 8,0,2 = 5 triangles
    1,2,3 / 1,4,6 / 6,7,10 / 10,8,9 / 9,5,3 = 5 triangles
    2,0,7,8,10 / 4,0,8,5,9 / 7,0,5,2,3, / 8,0,2,4,1 / 5,0,4,7,6 = 5 triangles

    Answer:   35 triangles

17)

Answer:

     5 totally clear days and 15 half and half.
     
     In the 15 half and half days:
     7 <= 12 of the clear mornings were followed by rain,

     8 <= 13 of the clear afternoons were preceeded by rain.

     20 days of the vacation.

18)

Answer:

               counter       Possible   
               weights       loads
               10kg           10
               20kg           20
               40kg           30
               80kg           40
              160kg           50
                              60
                              70
                              80
                              90
                             100
                             110
                             120
                             130
                             140
                             150
                             160
                             170

19)

Answer:

        Trial and error

        [(2 * 3 + 8)/2] - 6 = 1  <- NO
        [(6 * 3 + 8)/2] - 6 = 7  <- NO
        [(8 * 3 + 8)/2] - 6 = 10 <- NO
        [(4 * 3 + 8)/2] - 6 = 4  <- YES!!  The number is 4

Algebraically: [(3*x + 8)/2] -6 = 4

20)

Answer:

     Find a pattern.

     2 steps        3 cubes             2 + 1
     3 steps        6 cubes             3 + (2 + 1)
     4 steps       10 cubes             4 + (3 + 2 + 1)
     5 steps

     9 steps       45 cubes             9 + (8 + 7 + 6 + 5 + 4 + 3 + 2 + 1)

     You will need 45 cubes.

21)

Answer:

          4 = 2 + 2
              2 * 2 = 4
          5 = 2 + 3
              2 * 3 = 6


        4       5       9       13      10      15      16      3       7
        2       2       4       7       5       7       7       1       3
        2       3       5       6       5       8       9       2       4
        4       6       20      42      25      56      63      2       12

22)

Answer:

     1 unit left and 3 units left.

23)

Answer:

24)

Answer:

          12 - 7 = 5 people in bare feet!

25)

Answer:

     Each day the grasshopper goes 1/8 m until the day when the 
     grasshopper is at 1.75m in morning, he gets out of the hole that 
     day.  1.75/(1/8)=14  and 14 + 1 = 15 days.

26)

Answer:

        Race Number             Position

K       5  (17)  (1) 7          (1) 2 3 4 
RA      5  (17)  (1) 7          1 (2) 3(4)
J       5  17     1  7          1  2  3(4)

Ri      5  17     1  7          1  2 (3)4


     1 and 17 are female -- from clue 1 and 3
     5 and 7 are male -- from above
     J did not come 3rd -- from clue 5
     17 is not first -- from clue 1
     Kim is not first.
     Rick finished before 7, therefore he must be 5
     after Raelene who was first,
     therefore, 
     Raelene is #1 and first
     Rick is #5 and second
     Kim is #17 and third
     Jim is #7.

27)

Answer:

     The number of children = number of different combinations of
     two different flavours.


        1,2     2,3     3,4     4,5     5,6     6,7     7,8     8,9
        1,3     2,4     3,5     4,6     5,7     6,8     7,9
        1,4     2,5     3,6     4,7     5,8     6,9
        1,5     2,6     3,7     4,8     5,9
        1,6     2,7     3,8     4,9
        1,7     2,8     3,9
        1,8     2,9
        1,9


               36 = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

               There are 36 children.

28)

Answer:

     [9][5] * [7][6] + [4] * [1] = 7224

29)

Answer:

     Must earn 4 x $1,000.00 + 4 x $152.00= 4608

     Number of houses = 4608/$256/house 
                      = 18 houses.

30)

Answer:

          2 + 3(2) + 5(2) = 18

          18($200.00) = $3600.00

31)

Answer:

     How many numbers between 1 and 18 are multiples of 2 and 3?
                6, 12, 18

     [ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o]

                       1                   2                   3


     There will only be 3 lily pads that both frogs jump on
     - Number 6, 12 and 18.

32)

Answer:

     489 divided by 6 equals 81 with a remainder of 3

     He casn sell 81 bunches, which wuld leave him 3 to sell at regular
     price.

33)

Answer:

     110 divide by 95 equals 1 with a remainder of 15  cookies
     130 divide by 95 equals 1 with a remainder of 35  fudge
     116 divide by 95 equals 1 with a remainder of 21  squares 
     110 - 95 = 15 cookies
     130 - 95 = 35 fudge
     116 - 95 = 21 squares

     The students kept 15 cookies, 35 pieces of fudge and 21
     squares.

34)

Answer:

     A rectangle = (5-1)(4-1) = (4)(3) = 12
     - each shaded area.

     (1)        (3-1)(2-1) = (2)(1) = 2
     (2)        (4-2)(3-2) = (2)(1) = 2
     (3)        (5-4)(4-3) = (1)(1) = 1
     (4)        (3-2)(4-3) = (1)(1) = 1

                                      6


     Area shaded / Area of rectangle = 6/12 = 1/2

35)

Answer:

     ROUND          PLAYERS REMAINING        GAMES


       1                     16                8
       2                   16 - 8              4
       3                    8 - 4              2
       4                    4 - 2              1 
                                              ----
                                               15

36)

Answer:

     Time for Man                  Time for Wife


     6km / 4km/hr                  6km / 5km/hr 
     =                             =
     3/2 * 60min                   6/5 * 60min
     =                             =
     90 minutes                    72 minutes


     As the woman will get there first, she will have to wait for 
     the man.  The time taken to meet will be 90 minutes.

37)

Answer:

     (1)  [1] - [2] - [3]

     (2)  [2] - [3] - [1]

     (3)  [3] - [2] - [1]

     (4)  [2] - [1] - [3]

     (5)  [3] - [1] - [2]

     (6)  [1] - [3] - [2]

     There are three different ways.

38)

Answer:

     $9.75 - $8.00 = $1.75

     $1.75/$0.25/yr = 7 years

     Therefore, 1989 + 7 = 1996

39)

Answer:

     
        Only Jam        Only Peanut Butter      Jam/Peanut Butter
        35 - 30              41 - 30                    30
           5                    11


     Number that liked neither = 50 - (5+11+30) = 4

40)

Answer:

     72/18 = 4

     18/72 = 1/4

     18/72 + 1/72 = 1/4 + 1/72 = 19/72

41)

Answer:

     In a full cube 3 x 3 x 3 = 27

     There are 5 missing cubes, therefore there are 22 cubes needed to 
     build this figure.

42)

Answer:

             123  234   345
             124  235
             125  245
             134
             145


     There are 10 possible triangles.
     Each will be used 6 times.

43)

Answer:

     (3/10)*? = 24  and 24/(3/10) = 80.    

     Aunt Helen is 80 years old.

44)

Answer:

          3/5(3/5)(100)   3/5(3/5)(3/5)(100)

     
     (1)       (2)         (3)
     100 + 2(3/5)(100) + 2(3/5)(3/5)(100) + 2(3/5)(3/5)(3/5)(100)
     + 2(3/5)(3/5)(3/5)(100) = 

     100 + 600/5 + 1800/25 + 5400/125 + 16200/625

               = 361.12m

45)

Answer:

               $56.97
                83.29
                41.96
              + 37.47
             ---------
              $219.69

          1/2(219.69) = 109.85


     $109.85 - (Clare's payment) = $30.42 = amount Clare owes Mary.

46)

Answer:

     1min/55 * 14500 = 263.64 min
                     = 4h 23.64 min.

47)

Answer:

4 * 3/9 = 12/9 = 4/3 = AB

48)

Answer:

243/2 = 121.5

121.5 pages are whole numbers therefore the pages are 121 and 122