A pen and 2 erasers cost $6.80. A pen and 5 erasers cost $12. Let: P = cost of 1 pen E = cost of 1 eraser Using the first equation: P + 2E = $6.80 Using the second equation: P + 5E = $12 Solving the two equations simultaneously: P + 2E = $6.80 P + 5E = $12 Subtracting the equations: 3E = $12 - $6.80 = $5.20 E = $5.20/3 = $1.60 Substitute E

1. Heuristics & Key Concepts
Stacking Models 1
Level 1

2. Stacking models
Tips :
1)Question has 2 or more items. At least
there are more than 1 copy of each item.
Eg : 2 chairs and 3 tables

3. Stacking Models 1
1) A table and 2 chairs cost $215. The table
costs 3 times as much as a chair. Find the cost
of the table.
?
table
$215
chair
chair
(Total) 5 units → $215
1 unit → $215 ÷ 5 = $43
(Table) 3 units → 3 X $43 = $129
Ans : $129

4. Practice 2 Stacking Models 1
1) Rani paid $224 for 2 boxes of mangoes and 3
boxes of apples. A box of mangoes cost twice as much
as a box of apples. Find the cost of each box of
apples?
mangoes
mangoes
apples $224
?
apples
apples
(Total) 7 units → $224
1 unit (apples) → $224 ÷ 7 = $32
Ans : $32

5. Practice 2 Stacking Models 1
2) Edward paid $520 for 3 ties and 8 shirts. A tie
cost 4 times as much as a shirt. Find the cost of each
tie. ?
tie
tie
tie
shirt
shirt $520
shirt (Total) 20 units→ $520
shirt 1 unit (shirt)→ $520 ÷ 20
shirt = $26
shirt 4 units (shirt)→ $26 x 4
shirt = $104 Ans : $104
shirt

6. Practice 2 Stacking Models 1
3) Mr Teo bought a visualiser and 2 cameras for
$7 500. The visualiser cost half as much as camera.
Find the cost of each visualiser.
visualiser ?
$7 500
camera
camera
(Total) 5 units → $7 500
1 unit (visualiser) → $7 500 ÷ 5 = $1 500
Ans : $1 500

7. Practice 2 Stacking Models 1
4) Jane has enough money to buy either 6 markers or
12 pens. If she buys 8 pens, how many markers can
she buy with the remaining money?
markers
pens
Remaining
money
4 pens  2 markers
Ans : 2

8. Practice 2 Stacking Models 1
5) Daniel could buy 8 apples and 5 peaches with $8.
He could buy 16 such apples with the same amount of
money. If he decided to buy peaches only, how many
peaches could he buy with $100?
$8
$4 $4
16 apples  $ 8
8 apples  $ 4 (5 peaches)
$4  5 peaches
$100  100 x 5 = 125 Ans : 125
4

9. Heuristics & Key Concepts
Multiples & Comparison
Models 1
Level 2

10. Multiples & Comparison Models 1
Tips :
1) Look for comparison terms such as
‘more than’, ‘less than’, ‘shorter than’, ‘longer than’, ‘taller
than’, ‘heavier than’, ‘lighter than’ etc.
2) Look for terms such as
‘twice as much as’, 3 times as many as’ etc.
3) All the bars will be of different no. of units. But each
unit is of the same size. Hence solving multiples model is
easier than solving comparison model.
4) Start labelling first and then draw the bars in
different lengths.

11. Multiples & Comparison Models 1
Harry has 2 times as much savings as Aaron.
Mike has $3087 more than Aaron. They have a
total savings of $13 259. How much savings
does Mike have?
Harry
$13 259
Aaron
Mike $3087
?
4 units → $13 259 - $3087 = $10 172
1 unit → $10 172 ÷ 4 = $2543
Mike → $2543 + $3087 = $5630
Ans : $5630

12. Practice 4 Multiples & Comparison Models 1
1) Jason, William and Joyce share $120.
William gets $16 more than Jason. Joyce gets
twice as much money as William. How much
money does William get?
Joyce
William ? $120
Jason $16
$120 + $16 = $136
4 units → $136 (total)
1 unit → $136 ÷ 4 = $34 (William)
Ans : $34

13. Practice 4 Multiples & Comparison Models 1
2) A hawker sold 1 090 cans of drinks in 3
days. He sold 110 more cans on Day 1 than on
Day 2.On Day 3, he sold thrice as many cans as
Day 1.How many cans of drinks did he sell on
Day 1?
Day 3
Day 1 ? 1 090
Day 2 110 cans
1 090 + 110 = 1 200
5 units → 1 200 (total)
1 unit → 1 200 ÷ 5 = 240 (Day 1) Ans : 240

14. Practice 4 Multiples & Comparison Models 1
3) Ann, Jane and Nelson have a total of 188
comic books. Ann has twice as many as comic
books as Jane. Nelson has 24 fewer comic
books than Jane. How many comic books does
Nelson have?
Ann
Jane 188 books
Nelson ? 24
188 + 24 = 212
4 units → 212 (total)
1 unit → 212 ÷ 4 = 53 (Jane)
53 – 24 = 29 (Nelson) Ans : 29

15. Practice 4 Multiples & Comparison Models 1
4) Three girls have a total of 72 dolls. Gena
has 3 times as many dolls as Jessie. Prema
has 7 more dolls than Jessie. How many dolls
does Prema have?
Gena
Jessie 7
72 dolls
Prema ?
72 - 7 = 65
5 units → 65 (total)
1 unit → 65 ÷ 5 = 13 (Jessie)
13 + 7 = 20 (Prema) Ans : 20

16. Practice 4 Multiples & Comparison Models 1
5) Ian, Thomas and Josh have a total of 264
phone cards. Ian has thrice as many phone
cards as Thomas. Josh has 30 fewer phone
cards than Ian. How many phone cards does
Josh have?
Ian
Thomas ? 30
264 dolls
Josh
264 + 30 = 294
7 units → 294 (total)
1 unit → 294 ÷ 7 = 42 (Thomas)
3 units → 42 x 3 = 126 (Ian)
126 – 30 = 96 Ans : 96

17. Before & after model – equal stage
Tips :
For Equal stage, normally we start drawing
model from the equal stage. However, for
internal transfer, we should start drawing
from the ‘Before’.
Internal transfer
Tips :
In internal transfer, both quantities
change in before and after scenarios, but
the total is unchanged.

18. Heuristics & Key Concepts
Before & after model – equal
stage 1 (1 quantity unchanged)

19. Before & after model – equal stage
Tips :
For Equal stage, always start drawing
model from the equal stage, except for
internal transfer where we should start
drawing from the ‘Before’.
1 quantity unchanged
Tips :
Identify the quantity that is unchanged.

20. Before & after model – equal stage 1 (1 quantity unchanged)
1) Harry and Calvin had the same amount of
money. Calvin spent $96. In the end, Harry had
4 times as much as Calvin. How much did Harry
have?
4 units = $?
Harry Note : Harry’s $ is
unchanged.
Calvin Spent $96
1 unit 3 units
3 units → $96
1 unit → $96 ÷3 = $32
(Harry) 4 units → 4 X $32 = $128
Ans : $128

21. Before & after model – equal stage 1 (1 quantity unchanged)
2) Ben and Ken had the same amount of money.
Ken spent $146. In the end, Ben had 3 times as
much as Ken. How much did Ben have?
3 units = $?
Ben Note : Ben’s $ is
unchanged.
Ken Spent $146
1 unit 2 units
2 units → $146
1 unit → $146 ÷ 2 = $73
(Ben) 3 units → 3 X $73 = $219
Ans : $219

22. Before & after model – equal stage 1 (1 quantity unchanged)
3) Rick and Stan had the same amount of
money. Stan spent $308. In the end, Rick had
8 times as much as Stan. How much did Rick
have?
8 units = $?
Rick Note : Rick’s $ is
unchanged.
Stan Spent $308
1 unit 7 units
7 units → $308
1 unit → $308 ÷7 = $44
(Rick) 8 units → 8 X $44 = $352
Ans : $352

23. Before & after model – equal stage 1 (1 quantity unchanged)
4) Sally and Mabel had the same number of
cards at first. After Sally gave 18 of her
cards, Mabel had 4 times as many cards as
Sally. How many cards did each girl have at
first?
4 units = ?
Mabel Note : Mabel’s
number of cards is
Sally Gave 18 cards unchanged.
1 unit 3 units
3 units → 18
1 unit → 18 3 = 6
(At first) 4 units → 4 X 6 = 24
Ans : Mabel: 24
Sally: 24

24. Heuristics & Key Concepts
Before & after model – equal
stage (internal transfer)

25. Before & after model – equal stage
Tips :
For Equal stage, normally we start drawing
model from the equal stage. However, for
internal transfer, we should start drawing
from the ‘Before’.
Internal transfer
Tips :
In internal transfer, both quantities
change in before and after scenarios, but
the total is unchanged.

26. Before & after model – equal stage 2 (internal transfer)
1) Jack and Rick had the same amount of
money. After Jack gave $49 to Rick, Rick had
3 times as much as Jack. How much did Rick
have in the end?
1 unit
Internal transfer –
J $49 total is unchanged
Internal transfer –
R $49
Start drawing from
‘before’
1 unit
2 units → $49 x 2 = $98
J 2 units 1 unit → $98 2 = $49
(Rick in the end) 3 units → 3 X $49
R $49 $49 = $147
Ans : $147
3 units

27. Before & after model – equal stage 2 (internal transfer)
2) Vince and Stan had the same amount of
money. After Vince gave $90 to Stan, Stan
had 7 times as much as Vince. How much did
Stan have in the end?
1 unit
Internal transfer –
V $90 total is unchanged
Internal transfer –
S $90
Start drawing from
‘before’
1 unit
6 units → $90 x 2 = $180
V 6 units 1 unit → $180 6 = $30
(Stan in the end) 7 units → 7 X $30
S $90 $90 = $210
Ans : $210
7 units

28. Before & after model – equal stage 2 (internal transfer)
3) Stan and Aaron had the same amount of
money. After Stan gave $36 to Aaron, Aaron
had 5 times as much as Stan. How much did
Aaron have in the end?
1 unit
Internal transfer –
S $36 total is unchanged
Internal transfer –
A $36
Start drawing from
‘before’
1 unit
4 units → $36 x 2 = $72
S 4 units 1 unit → $72 4 = $18
(Aaron in the end) 7 units → 5 X $18
A $36 $36 = $90
Ans : $90
5 units

29. Heuristics & Key Concepts
Repeated Identity
Level 1

30. Repeated Identity
Tips :
Draw 2 types of model
 Part whole model
 Comparison model
1 quantity is repeated
Tips :
Identify the quantity that is repeated.

31. Repeated Identity
Hari and Faridth have $120. Hari and Peter
have $230. Peter has 6 times as much money
as Faridth. How much money does Hari have?
$120 $110 Repeated Identity
Hari Faridth
1 unit 5 units
$230 5 units → $10
1 unit (Faridth) → $110 5
Hari Peter
= $22
6 units
Hari → $120 - $22 = $98
Ans : $98

32. Repeated Identity
A basket with 65 sweets has a mass of 3 200g.
The same basket with 40 sweets has a mass of
2 125g. Each sweet has the same mass. What is
the mass of the basket?
2 125g 1 075g Repeated Identity
basket 40 sweets
25 sweets → 1 075g
25 sweets 1 sweet → 1 075g 25
3 200g = 43g
40 sweets → 40 x 43 g
basket 65 sweets = 1 720g
Basket → 2125 -1720
= 405g
Ans : 405g

33. Repeated identity
1) Oscar has 2 times as much as Tom’s
money. Gary has 2 times as much as Oscar's
money. They have $5.25 altogether. How
much does Gary have?
?
Gary
Oscar $5.25
Tom
Total units → 1 + 2 + 4 = 7 units
1 unit → $5.25 ÷ 7 = $0.75
Gary → 4 units → 4 X $0.75 = $3
Ans : $3

34. Repeated identity
2) Ben has 2 times as much as Tom's money.
Leon has 3 times as much as Ben's money.
They have $3.15 altogether. How much does
Leon have?
?
Leon
Ben $3.15
Tom
Total units → 1 + 2 + 6 = 9 units
1 unit → $3.15 ÷ 9 = $0.35
Leon → 6 units → 6 X $0.35 = $2.10
Ans : $2.10

35. Repeated identity
3) Oscar has 4 times as much as Nick's money.
Fred has 3 times as much as Oscar's money.
They have $12.75 altogether. How much does
Fred have?
?
Fred
Oscar $12.75
Nick
Total units → 1 + 4 + 12 = 17 units
1 unit → $12.75 ÷ 17 = $0.75
Fred → 12 units → 12 X $0.75 = $9
Ans : $9

36. Heuristics & Key Concepts
Simultaneous Equation 1
Level 3

37. Simultaneous concept
2 or more items, 2 relationships
Strategy Used :
1) Draw model
2) Draw pictures
3) Use Alphabet method, to replace 1 of the items (usually the
unwanted item)- mostly used

38. Simultaneous Equation 1
1) A pen and 2 erasers cost $6.80.
A pen and 5 erasers cost $9.20. How much do
7 pens cost?
$6.80
pen 2 erasers
pen 5 erasers
? $9.20
3 erasers → $9.20 - $6.80 = $2.40
1 eraser → $2.40 3 = $0.80
2 erasers → 2x$0.80 = $1.60
1 pen → $6.80 – $1.60 = $5.20
7pens → 7 x $5.20 = $36.40
Ans : $36.40

39. Solution 2 Simultaneous Equation 1
2) A pen and 2 erasers cost $5.
A pen and 8 erasers cost $8.60. How much do
7 pens cost?
$5
pen 2 erasers
pen 8 erasers
? $8.60
6 erasers → $8.60 - $5 = $3.60
1 eraser → $3.60 6 = $0.60
2 erasers → 2x$0.60 = $1.20
1 pen → $5 – $1.20 = $3.80
7pens → 7 x $3.80 = $26.60
Ans : $26.60

40. Simultaneous Equation 1
3) A pen and 4 erasers cost $8.90.
A pen and 6 erasers cost $10.70. How much do
5 pens cost?
$8.90
pen 4 erasers
pen 6 erasers
? $10.70
2 erasers → $10.70 - $8.90 = $1.80
1 eraser → $1.80 2 = $0.90
4 erasers → 4 x $0.90 = $3.60
1 pen → $8.90 – $3.60 = $5.30
5 pens → 5 x $5.30 = $26.50
Ans : $26.50

41. Simultaneous Equation 1
A box of chalks and 2 dusters cost $10.
3 boxes of chalk and 2 dusters cost $18.
Find the total cost of 1 box of chalk and 1
duster.
$10
2 dusters 1 box of chalk
2 dusters 3 boxes of chalk
$18
2 boxes of chalk → $18 - $10 = $8
1 box of chalk → $8 2 = $4
2 dusters → $10 - $4 = $6
1 duster → $6 2 = $3
1 box of chalk and 1 duster → $4 + $ 3 = $7
Ans : $7

42. P4 Heuristics & Key Concepts
Gaps & Intervals

43. Gaps & Intervals
Tips :
1) Involves equal distance bet. trees, lamp
post, seedlings etc.
2) To find the no. of intervals, use the 2nd no.
to subtract the first no. Trs, please draw a
diagram to illustrate.
Eg : Tree No. 3 to Tree no. 7→ 7 - 3 = 4 gaps
Tree No.1 to Tree no. 6 →6 - 1 = 5 gaps
Tree 1 2 3 4 5 6 7
3) No. of trees → No. of gaps + 1.

44. Gaps & Intervals
1) Every lamp post is numbered. The distance
from lamp post number 3 to lamp post number
28 is 1.125 km. Find the distance from the first
lamp post to lamp post number 4 in metres.
No. of gaps fr lamp post 3 to 28 → 28 – 3 = 25
1 gap→ 1125m ÷ 25 = 45m
Number of gaps fr lamp post 1 to 4 → 4 - 1 = 3
Distance → 3 X 45m = 135m
Ans : 135m

45. Gaps & Intervals
2) Every lamp post is numbered. The distance
from lamp post number 5 to lamp post number
55 is 1.25 km. Find the distance from the first
lamp post to lamp post number 5 in metres.
No. of gaps fr lamp post 5 to 55 → 55 – 5 = 50
1 gap→ 1250m ÷ 50 = 25m
Number of gaps fr lamp post 1 to 5 → 5 - 1 = 4
Distance → 4 X 25m = 100m
Ans : 100m

46. Gaps & Intervals
3) Every lamp post is numbered. The distance
from lamp post number 9 to lamp post number
54 is 1.575 km. Find the distance from the first
lamp post to lamp post number 7 in metres.
No. of gaps fr lamp post 9 to 54 → 54 – 9 = 45
1 gap→ 1575m ÷ 45 = 35m
Number of gaps fr lamp post 1 to 7 → 7 - 1 = 6
Distance → 6 X 35m = 210m
Ans : 210m

47. Heuristics & Key Concepts
‘Sets ’Concept 1

48. Set Concept 1
Tips :
1) Identify the number of items in 1 set.
2) Take total number of items number of
items in 1 set.
3) The remainder will be the items that don’t
belong to the set.

49. ‘Sets’ concept 1
2) Pens are sold in packets of 5 pens. Each
packet is sold at $7. Gopal has $30. How many
pens can he buy at most?
1 set  $7
$30 ÷ $7 = 4 r $2 → Does not belong to set
→
Number of sets
1 set  5 pens
4 sets 4 x 5= 20
Ans : 20

50. ‘Sets’ concept 1
1) A sweet cost 15 cents and a packet of 8
similar sweets cost $1. Clement bought exactly
37 sweets. What was the least amount of
money that Clement spent on the sweets?
1 set → 8 sweets
37 ÷ 8 = 4 r 5 → Does not belong to set
→
Number of sets
1 set  $1 1 sweet  $0.15
4 sets 4 x $1 = $4 5 sweets 5 x $0.15 = $0.75
Total amount  $4 + $0.75 = $4.75 Ans : $4.75

51. Heuristics & Key Concepts
‘Sets ’Concept 2

52. ‘Sets’ concept 1
1) Fred bought as many pens as staplers.
A pen costs $3.80 while a stapler costs $3.20.
Fred paid $21. How many staplers did he buy?
1 set → 1 pen + 1 stapler
→ $3.80 + $3.20 = $7
Number of sets → 21 ÷ 7 = 3
Ans : 3

53. ‘Sets’ concept 1
2) Gary bought as many pens as staplers.
A pen costs $4.90 while a stapler costs $4.10.
Gary paid $72. How many staplers did he buy?
1 set → 1 pen + 1 stapler
→ $4.90 + $4.10 = $9
Number of sets → 72 ÷ 9 = 8
Ans : 8

54. ‘Sets’ concept 1
3) Oscar bought as many pens as staplers.
A pen costs $2.80 while a stapler costs $2.20.
Oscar paid $15. How many staplers did he buy?
1 set → 1 pen + 1 stapler
→ $2.80 + $2.20 = $5
Number of sets → 15 ÷ 5 = 3
Ans : 3

55. Heuristics & Key Concepts
‘Sets ’ Concepts 3

56. ‘Sets’ concept 2
1) A packet of apples has a mass of 1.1 kg.
A packet of papayas has a mass of 5.9 kg.
9 more packets of apples than papayas are
sold. The total mass of both fruits sold is 51.9
kg. How many packets of apples are sold?
9 more packets of apples → 9 X 1.1 kg = 9.9 kg
Remaining → 51.9 kg - 9.9 kg = 42 kg
1 set → 1 packet of apples + 1 packet of papayas
→ 1.1 kg + 5.9 kg = 7 kg
Number of sets → 42 ÷ 7 = 6
Packets of apples sold → 9 + 6 = 15
Ans : 15

57. ‘Sets’ concept 2
2) A packet of oranges has a mass of 3.3 kg.
A packet of papayas has a mass of 2.7 kg.
8 more packets of oranges than papayas are
sold. The total mass of both fruits sold is 44.4
kg. How many packets of oranges are sold?
8 more packets of oranges→ 8 X 3.3 kg = 26.4 kg
Remaining → 44.4 kg – 26.4 kg = 18 kg
1 set → 1 packet of oranges + 1 packet of papayas
→ 3.3 kg + 2.7 kg = 6 kg
Number of sets → 18 ÷ 6 = 3
Packets of oranges sold → 3 + 8 = 11
Ans : 11

58. ‘Sets’ concept 2
3) A packet of papayas has a mass of 1.3 kg.
A packet of pears has a mass of 0.7 kg.
2 more packets of papayas than pears are sold.
The total mass of both fruits sold is 14.6 kg.
How many packets of papayas are sold?
2 more packets of papayas→ 2 X 1.3 kg = 2.6 kg
Remaining → 14.6 kg – 2.6 kg = 12 kg
1 set → 1 packet of papayas + 1 packet of pears
→ 1.3 kg + 0.7 kg = 2 kg
Number of sets → 12 ÷ 2 = 6
Packets of papayas sold → 6 + 2 = 8
Ans : 8

59. Heuristics & Key Concepts
‘Sets ’Concept 3( More Qns)

60. ‘Sets’ concept 2 (more qns)
1) A book costs $3.20. A file costs $1.80.
8 more books than files are bought.
The total cost is $55.60. How many books are
sold?
8 more books → 8 X $3.20 = $25.60
Remaining → $55.60 - $25.60 = $30
1 set → 1 book + 1 file
→ $3.20 + $1.80 = $5
Number of sets → 30 ÷ 5 = 6
Books sold → 6 + 8 = 14
Ans : 14

61. ‘Sets’ concept 2 (more qns)
2) A book costs $4.70. A file costs $3.30.
3 more books than files are bought.
The total cost is $86.10. How many books are
sold?
3 more books → 3 X $4.70 = $14.10
Remaining → $86.10 - $14.10 = $72
1 set → 1 book + 1 file
→ $4.70 + $3.30 = $8
Number of sets → 72 ÷ 8 = 9
Books sold → 9 + 3 = 12
Ans : 12

62. ‘Sets’ concept 2 (more qns)
3) A book costs $3.50. A file costs $2.50.
5 more books than files are bought.
The total cost is $29.50. How many books are
sold?
5 more books → 5 X $3.50 = $17.50
Remaining → $29.50 - $17.50 = $12
1 set → 1 book + 1 file
→ $3.50 + $2.50 = $6
Number of sets → 12 ÷ 6 = 2
Books sold → 2 + 5 = 7
Ans : 7

63. Heuristics & Key Concepts
Rearrange Concept
(Total remains
unchanged)

64. Rearrange
Concept
Tips :
1) Two quantities will be given, example:
pupils, eggs
2) One of the two quantities will either
increase or decrease.
3) The other quantity remains the same.

65. Rearrange Concept
1) Books in a library were placed on 30 shelves with
an equal number of books on each shelf. 3 shelves
were removed and the books on the these shelves
were placed on the remaining 27 shelves. The number
of books on each shelf increased by 5. How many
books are there altogether?
30 Units Note:
number of
3 units Books does
not change
27 Units 27 x 5=135
3 units  135 books
1 unit 135 ÷ 3= 45
30 units  30 x 45 =1 350 Ans : 1 350

66. Rearrange Concept
2) 40 boys had to paint some Easter eggs. One
of the fell sick and the other boys had to paint
3 more Easter eggs each. How many Easter
eggs did they paint altogether?
Note:
40 Units
number of
1 unit eggs does
not change
39 Units 39 x 3=117
1 unit  117 eggs
40 units 40 x 117= 4 680
Ans : 4 680

67. Heuristics & Key Concepts
Constant Difference

68. Constant Difference
Tips :
1) The difference between ages always remains
unchanged.
2) The difference between two or more items
remains unchanged (before and after) if
there is an
 increase of the same amount for each item
 decrease of the same amount for each item

69. Constant Difference
Tips :
1) When drawing the models, put the
actual values (given at first) at the back
of the part whole model.
2) The equal amount should be placed in
the front.
 For age questions, the equal amount is
the number of years. (i.e. how many
years later or before)

70. Constant Difference– Age question
IEXCEL Unit 5
Q2. Mr Kumar is 44 years old now and his son is 18 years old.
How many years later will Mr Kumar be twice as old as his son?
2 units
Mr Kumar ?
44
1 unit 44 – 18 = 26
Son ?
18 1 unit
1 unit → 26
26 -18 = 8
Ans : 8

71. Constant Difference– Increase/Decrease same value
IEXCEL Unit 5
Q4. Aileen had $82 and Casey had $26 at first. Each of them
bought a concert ticket of the same price. After that, Aileen
had 5 times as much money left as Casey. How much did each
ticket cost?
$82
Aileen ?
5 units
$26 $82 – $26 = $56
Casey ?
1 unit 4 units
4 units → $56
1 units → $56 ÷ 4 = $14
$26 - $14 = $12 Ans : $12

72. Heuristics & Key Concepts
Before & after model – equal
stage 2 (External Unchanged)

73. Before & after model – equal stage 2
(external unchanged)
Tips :
1) For Equal stage, always start drawing
model from the equal stage.
2) External Unchanged – items will have
an increase/decrease of different
values.

74. Before & after model – equal stage 2 (external unchanged)
IEXCEL Unit 6
Q2. Helen and Jessie went shopping with an equal amount of
money. Helen spent $70 and Jessie spent $250. After that,
Helen had thrice as much as money left as Jessie. How much
money did each girl bring along for shopping?
?
3 units
Helen $70 Note : 3 units – 1 unit = 2
unit
2 units
2 units $250 - $70 =
Jessie $180 $70
$180 (constant
difference)
1 unit $250
2 units → $180
1 unit → $180 ÷ 2 = $90
3 units → $90 x 3 = $270
$270 + $70 = $340 Ans : Helen: $340
Jessie: $340

75. Before & after model – equal stage 2 (external unchanged)
IEXCEL Unit 6
Q4. Alvin and Sam received an equal amount of money. Alvin
spent $35 and Sam spent twice as much as Alvin. After that,
Alvin’s remaining money was twice as much as that of Sam’s.
How much money did each boy receive at first?
?
2 units
Note : 2 units – 1 unit = 1
Alvin $35 unit
Sam $35 $35 1 unit $35x 2 -$35 =
1 unit 1 unit $35 (constant difference)
1 unit → $35
3 units → 3 X $35 = $105
Ans : Alvin: $105
Sam: $105