Category Archives: Problem Sums

Primary 6 August Problem Sums 9

P6-PSP-Aug-Ex 9

Ans:

1– 28 cm

Square num­bers are 1, 4, 9, 16, 25, 36, 49, 64, 81, etc …

The two pos­si­ble square num­bers that add to 74 are 25 and 49

5 cm × 5 cm = 25 cm²

7 cm × 7 cm = 49 cm²

7 cm × 4 = 28 cm

 

2–  355 more marbles

Num­ber of boys –>  3 + 5 = 8

Units of mar­bles each girl received –> 1u

Units of mar­bles each boy received –>  1u + 30

Total received by the 8 chil­dren –>  1u × 3 + (1u + 30) × 5 = 8u + 150

8u + 150 mar­bles ->  570 marbles

8u –>  570 — 150 = 420 marbles

1u –>  102.5 marbles

(5u + 150) — 3u = 2u + 150

(102.5 × 2) + 150 = 355 more marbles

 

3–  $71.50

7 duri­ans + 10 man­goes –> $57

[1 durian + 1 mango –>  $7.50] × 7
–>  7 duri­ans + 7 man­goes –>  $52.50

There­fore, $57 — $52.50 = $4.50 –>  3 mangoes

1 mango–>  $4.50/ 3 = $1.50

1 durian –>  $7.50 — $1.50 = $6

4 duri­ans + 3 man­goes –>  $6 × 4+ $1.50 × 3 = $28.50

$100 — $28.50 = $71.50

 

4–  15 : 6 : 10

Red   :  Blue                      Blue   :   Pur­ple
5      :     2                             3      : 5

–>  15    :     6                             6      : 10

Red   :   Blue   :   Pur­ple
15   :    6    : 10

 

5–  56 cm

Height of water level at first –>  5/8 × 64 cm = 40 cm

1600 cm³ ÷ (10 × 10) cm² = 16 cm

16 cm + 40 cm = 56 cm

 

6–  200 cook­ies

[Con­stant Difference]

At first:

Joanna –>  250 cookies

Sharon ->  350 cookies

In the end –>        Joanna  :  Sharon
3       : 5

2u –> 100

1u –> 50

8u –>  50 × 8 = 400 cook­ies left

600 — 400 = 200 cook­ies

 

7–  $13.50

5 small tow­els + 6 big tow­els –>  $34.50

6 small tow­els + 5 bog tow­els –>  $34.50 — $4 = $31.50

11 small tow­els + 11 big tow­els –>  $34.50 + $31.50 = $66

1 small towel + 1 big towel –> $66/ 11 = $6

5 small tow­els + 5 big tow­els –>  $6 × 5 = $30

1 big towel –> $34.50 — $30 = $4.50

$4.50 × 3 = $13.50

Con­tinue read­ing

Primary 6 April Problem Sums 5

P6-PSP-Apr-Ex 5

Ans:

1–  30 m

Spaces between 100 trees –> 99

Dis­tance between each tree –> 297 m ÷ 99 = 3 m

3 m × 10 spaces = 30 m

 

2–  28 pupils

Num­ber of pupils who passed one or both sub­jects –> 40 — 2 = 38

30 + 36 = 66

66 — 38 = 28 pupils

 

3–  a ->  (18s + 24) kg ,   b ->   16 kg

Mass of chicken –>  3s kg

Mass of puppy –>  (3s + 4) kg

Mass of dog –>  (3+ 3s + 4) kg × 2 = (12+ 8) kg

3s + 3s + 4 + 12s + 8 = (18s + 12) kg                   (a)

18 × 2 + 12 = 48 kg

48 kg ÷ 3 = 16 kg                           (b)

 

4–  $51.30

Total cost of 5 apples and 5 man­goes –>  $3.25 × 5 = $16.25

Cost of 3 apples –>  $17.60 — $16.25 = $1.35

Cost of 1 apple –> $1.35 ÷ 3 = $0.45

Cost of 1 mango –> $3.25 — $0.45 = $2.80

Cost of 2 man­goes and 7 apples –>  $2.80 × 2 + $0.45 × 7 = $8.70

$50 — $8.70 = $51.30

Con­tinue read­ing

Primary 4 March Problem Sums 5

P4-PSP-Mar-Ex 5

Ans:

1–  $96

2–  28 sweets

Qn 2

If 1 add 12 more sweets to Jacque­line, she will have 1 unit.

4u –>  100 + 12 = 112

112 ÷ 4 = 28 sweets

 

3–  a ->  $8250   b ->  $2475

Amount of money Melanie spent in Jan­u­ary –>  $825 × 2 = $1650

$1650 × 5 = $8250          (a)

$825 + $1650 = $2475      (b)

 

4–  5/8 m

5– 1175 stamps

Roger –> 1u

Joshua –> 4u

4u — 1u = 3u

3u –>  705 stamps

1u –>  235 stamps

235 × 5u = 1175 stamps

Con­tinue read­ing

Primary 5 October Problem Sums 5

P5-PSP-Oct-Ex5

Ans:

1–  $6588

2–  2400 cm³

Amount of water at first –>  4/5 × 30 cm × 20 cm × 30 cm = 14 400 cm³

Amount of water in the end –>  2/3 × 30 cm × 20 cm × 30 cm = 12 000 cm³

14 400 cm³ — 12 000 cm³ = 2400 cm³

 

3–  38 mar­bles

Qn 3

2u –>  96 — 60 = 36

Barry –>  36 ÷ 2 = 18 marbles

Joe –>  60 — 18 = 42 marbles

Tom –>  18 × 3 = 54 marbles

Total –> 54 + 42 + 18= 114 marbles

114 ÷ 3 = 38 mar­bles

 

4–  Cup Y —  160 ml    ,   Cup Z —  60 ml

Y   :   Z
8   : 3

8u + 3 = 11u

11u ÷ 2 = 5.5u

8u — 5.5u = 2.5u

2.5u –>  50 ml

1u –>  20 ml

Cup Y –>  20 ml × 8u = 160 ml

Cup Z –>  20 ml × 3 = 60 ml

 

5–  $651.80

Qn 5

2u –>  $1505 — $201.40 = $1303.60

$1303.60 ÷ 2 = $651.80

 

6–  $15.50

Qn 6

 

2u–  $108 — $71 = $37

1u —  $18.50

Megan –> $18.50 × 3 = $55.50

$71 — $55.50 = $15.50

Con­tinue read­ing

Primary 6 September Problem Sums 10

P6-PSP-Sep-Ex 10

Ans:

1–  See below

Qn 1

 

2–  9360 cm³

Height of water needed to fill the con­tainer –>  25 cm — 18.5 cm = 6.5 cm

45 cm × 32 cm × 6.5 cm = 9360 cm³

 

3–  68 but­tons

36 + 3 = 39 more buttons

8 — 5 = 3  buttons

∴ She needs 39 more but­tons because she is putting 3 more but­tons into each box.

39 ÷ 3 = 13 boxes

13 × 5 + 3 = 68 but­tons

 

4–  $580

107% –>  $465.45

100% –>  $435 (dis­counted price with­out GST)

75% –> $435

100% –>  435/75 × 100 = $580

 

5–  136 chil­dren

40% = 40/100 = 2/5

2/3 of the boys = 2/5 of the girls

Boys  :  Girls
3      : 5

2u –> 34

1u –> 17

17 × 8 = 136 chil­dren 

Con­tinue read­ing

Primary 4 July Problem Sums 3

P4-July-PSP-Ex 3

Ans:

1–  $9153

$2178 + $6975 = $9153

 

2–  5  5/12 kg

The total mass of the nails–>  9   11/12 kg —   11/12 kg = 9 kg

Mass of the nails when they are half-filled –>  9 /2 = 4   1/2 kg

4   1/2 kg +  11/12 kg = 5   5/12 kg

 

3–  3456 canned drinks

128 × 27 = 3456 canned drinks

 

4–  56.58 kg

Qn 4

6u –>  169.74 kg

1u –>  28.29 kg

28.29 kg × 2 = 56.58 kg

Con­tinue read­ing

Primary 6 July Problem Sums 6

P6-July-PSP-Ex 6

Ans:

1–  $800

Frac­tion of money spent on food and shoes –>  1/4 + 1/5 = 9/20

20/20 — 9/20 = 11/20

11u –>  $340 + $100 = $440

1u –> $40

20u –>  $40 ×  20 = $800

 

2–  14 cook­ies

Muffins   :   Cookies

At first  ——>           [   5             :         6   ]  × 2

In the end   ——>    [   2             :        1  ]  × 5

[Make the units of muffins at first and in the end the same]

Muffins   :   Cookies

At first  ———>             10          : 12

In the end  ——->           10          : 5

12u –>  24 cookies

1u –>  2 cookies

5u –>  10 cook­ies left

24 — 10 = 14 cook­ies 

 

3–  Joseph spent more by $2000

3/5 of Terry’s money is equal to 1/3 of Joseph’s money.

[Make the numer­a­tor common]

3/5 of Terry’s is equal to  3/9 of Joseph’s.

Terry   :   Joseph
5         : 9

14u –> $7000

1u –> $500

Amount Terry spent –>  $500 × 5 = $2500

Amount Joseph spent –>  $500 × 9 = $4500

$4500 — $2500 = $2000

Con­tinue read­ing

Primary 4 July Problem Sums 2

P4-July-PSP-Ex 2

Ans:

1–  $144

1/2 u –> $36

1u –>  $36 × 2 = $72

$72 × 2 = $144

 

2–  $487.80

3–  6  4/5 kg

4–  2637 more seashells
Qn 4

7u –>  6328 — 623 = 5705

1u –> 815

Jan­ice –>  815 × 7 = 4075 seashells

Car­o­line –>  815 + 623 =1438 seashells

4075 — 1438 =  2637 more seashells

Con­tinue read­ing

Primary 6 July Problem Sums 5

P6-July-PSP-Ex 5

Ans:

1–  95

[Use trial and error from the largest 2-digit mul­ti­ple of 9]

Great­est pos­si­ble 2-digit mul­ti­ple of 9 –> 99

99 + 5 = 104 (wrong: answer is not 2-digit)

90 + 5 = 95 (correct)

 

2–  100 grey squares and + 99 white tiles

Num­ber of grey tiles –> Pat­tern Num­ber × 2

50 × 2 = 100 grey tiles

Num­ber of white tiles –>  Num­ber of grey tiles — 1

100 — 1 = 99 white tiles

 

3–  108 teach­ers

Pupils  –>                      Boys  :  Girls
4     : 5

5u –> 2400

1u –> 280

9u –>  280 × 9 = 4320 children

Teach­ers  :  Pupils
1          : 40

40u –> 4320

1u –>  108 teach­ers

 

4–  14 years old

Nicholas’ age now –>  35 — 8 = 27 years old

Timothy’s age now –>  1/3 × 27 = 9 years old

9 + 5 = 14 years old

Con­tinue read­ing

Primary 5 July Problem Sums 1

P5-July-PSP-Ex 1

Ans:

1–  $2425
Qn 1

1u –>  $1600 + $750 = $2350

$2350 + $750 = $2425

 

2–  29/45

Amount Diane saves -> $1800 — $640 = $1160

1160/1800 = 29/45

 

3–  4  1/2 kg

Mass of apples when the bas­ket is com­pleted filled –>  8 kg — 1 kg = 7 kg

Mass of apples when bas­ket is 1/2 filled –>  7 kg ÷ 2 = 3  1/2 kg

3  1/2 + 1  = 4  1/2 kg

 

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