A farmer had a twice as many chicken as ducks. After he had sold 200 chickens, he had thrice as many ducks as chickens. How many chickens did he have at first? Ans.: 240

chicken

ducksx

-200

6u – 1u -->5u --> 2001u --> 200 ÷ 5 = 40

200

2u

1u 3u

1ux 3 = 6u

x 3 = 3u

6u --> 6 x 40 = 240 (ans.)

Jane and Ivan had $60. After giving Ivan $8, Jane had the same amount of money as Ivan. How much money did Ivan have at first? Ans.: $22

Jane

Ivan

60+8

-8 1u

1u

60

2u -->1u --> 60 ÷

?

30

(30)

60 2 = 30

- 8 = 22 (ans.)

Thomas is 4 times as old as Sandra. Thomas will be twice as old as Sandra in 8 years time. How old is Thomas now? Ans.:16

Thomas

Sandra

4u

1u

+8

+8

2u

1u 1u3u x3=3u

x 3 =6u

x 3 =3u

6u – 4u --> 82u --> 81u --> 8 ÷ 2 = 4Thomas (now): 4u --> 4 x 4 = 16 (ans.)

John and Ramesh had an equal amount of sweets at first. John bought another 6 sweets and Ramesh lost 12 of her sweets. John had thrice as many sweets as Ramesh. Find the number of sweets each of them have first? Ans.:21

John

Ramesh

6

12

3u

1u

3u2u --> 18

1u --> 18Each (1st):

– 1u --> 12+ 6

÷ 2 = 91u +12 --> 9 +12 = 21 (ans.)

Some children were sharing oranges. If each child took 3 oranges, there would be 2 left over. But if each child took 4 oranges, there would be 2 oranges short. How many oranges were there? Ans.:14

Total

3 each2

4 each

2

4 each1 each --> 43 each --> 3

(12)

Total:

– 3 each --> 2 + 2

x 4 = 1212 + 2 = 14 (ans.)

A moment ago, Wendy had 2/5 as much money as Mike. Wendy withdrew $50 from her bank account. Now Wendy has 1/2 as much money as Mike.(a) How much money does Wendy have now? Ans.:$250(b) What was the total amount of money the two of them had a moment ago? Ans.: $700

Wendy

Mike

+50

x

2u

5u

1u

2u x 5 = 10u

x 5 = 5u

x 2 = 10u

x 2 = 4u

5u – 4u -->1u --> 50Wendy (now) 5u --> 5 xTotal (Before): 4u +14u --> 14 x

50

50 = 250 (ans.)10 u = 14u

50 = 700 (ans.)

Alex and his sister, Amber have a total of 120 computer games. If Alex gives Amber 5 games, Amber will have nine times as many games as Alex. How many more games does Amber have than Alex? Ans.: 86

Alex

Amber

-5

+59u

1u

120 120

1u + 9u -->10u --> 1201u --> 120 ÷Alex (1st): 1u +120

120

10 = 12 5 = 12 +5 = 17

– 17 = 103

17 ?

103

103 – 17 = 86 (ans.)

Olivia's mother was 4 times Olivia age 4 years ago. If their total age now is 48, how old is Olivia now? Ans.:12

mother

Olivia

4u

1u

4 years ago

+4

+4

now

4848 – 4

= 40

4u + 1u -->5u --> 401u --> 40 ÷Olivia (Now):

– 4

40

5 = 81u + 4 = 8 +4 = 12 (ans.)

A moment ago, 84 pears and 65 apples were displayed at a fruit stall. 28 pears were sold and some more apples were displayed. Now, 5 times as many apples as pears are displayed. How many apples have just been displayed? Ans.:215

A moment ago

pears

apples

84

65

-28

+? 5u

1u

Now

1u -->5u --> 5 x?:

84 – 28 = 5656 = 280

280 – 65 = 215 (ans.)

(280)

Mrs. Tay has a bag of sweets. If she gives each child 7 sweets, she will be left with 5 sweets. If she gives each child 9 sweets, she will need 5 more sweets.a)How many children are there? Ans.:5b)How many sweets are there? Ans.:40

Total

7 each5

9 each

5

9 each – 2 each --> 10

1 each --> 10 ÷7 each --> 7 x

(35)

Total: 35 +

7each --> 5 + 5

2 = 5 (a)5 = 35

5 = 40 (b)

Jason and Kevin were given some money each. If Jason and Kevin spent $100 and $50 each day respectively, Jason would have $1300 when Kevin had spent all his money. If Jason and Kevin spent $50 and $100 each day respectively, Jason would have $3700 when Kevin spent all his money. How much money was given to Jason in the beginning? Ans.:$4500

Jason

Kevin

-100 u

-50 u

1300

050u

100u 1300

Jason

Kevin

-50 p

-100p

3700

050u

100u 1300 ÷2

÷2

-25u

-50u

75u 1300

75u --> 3700 – 1u --> 2400 ÷Jason (1st): 100u +

1300 = 240075 = 32

1300 --> 100 x 32 + 1300 = 4500 (ans.)

Joe has 60% more marbles than Fred. First, Joe gave 20% of his marbles to Fred. In return, Fred gave 1/6 of his marbles to Joe. Finally, Fred had 80 fewer marbles than Joe. How many marbles did Joe have at first? Ans.:320

3/5 1/5

Joe

Fred

8u

5u

x 5 = 40u

x 5 = 25u

8/40

-8u

+8u

32u

33u-1/6-5.5u

+5.5u 37.5u

27.5u 80 10u

10u --> 801u --> 80 ÷ 10 = 840u --> 40 x 8 = 320 (ans.)

1u

When Mr Wong was Meimei's present age, she was 3 years old. When Meimei is Mr Wong's present age, he will be 81 years old.a)How much older is Mr Wong than Meimei? Ans.:26b)How old is Mr Wong now? Ans.:55

Wong

Meimei's

Present Was Future

3

81

1u 1u3 1u

3 2u

3 2u

2u + 1u -->3u --> 78

1u --> 78 ÷

3 1u

Wong (Now):

81 - 3

3 = 26 (a)3 +2u --> 3 + 2 x 26 = 55 (b)

Alex and Betty each had $600 at first. Alex spent $6 per day and Betty spent $2 per day. How long did it take for Betty's money to be twice as much as Alex's money? Ans.:60 days

Alex

Betty

600

600

-6 u

-2 u2p

1p

1p --> 600 2p --> 6002p --> 1200 – 12u

x2

1200

12u 2p

600

2u 2p

12u10u --> 600

1u --> 600 ÷

– 6u – 2u

– 2u -->1200 – 600

10 = 60 (ans.)

If Eddie uses his money to buy 7 similar bags, he will have $5 more than Alice. If Alice uses some of her money to buy same 7 bags, she will have $47 less than Eddie.a)Find the cost of 1 bag. Ans.:$3b)How much more money does Eddie have than Alice? Ans.:$26

Eddie 7 bags

Alice$5

7 bags

$47

7 bags + 7 bags -->14 bags --> 421 bag --> 42 ÷

47 - 5

14 = 3 (a)

?

7 bags --> 7 x21 +

3 = 215 = 26 (b)

Mr Tan had some apples and oranges in the ratio 4:5. After selling 170 apples and 25% of the oranges, the ratio of the apples to oranges left became 1:2. What was the number of fruits Mr Tan had in the end ? Ans.:450

apples

oranges

4u

5u

-170

-5u

1/4

x 4 = 20u

x 4 = 16u

5/20

15u

1p

2p x 7.5 = 15u

x 7.5 = 7.5u

16u – 7.5u -->8.5u --> 1701u --> 170 ÷Total (end): 7.5u +22.5u --> 22.5 x

170

8.5 = 2015u = 22.5u

20 = 450 (ans.)

Box A contained 350 black marbles and 500 white marbles. Box B contained 400 black marbles and 100 white marbles. After some black and white marbles were removed from Box B to be placed in Box A, 1/2 of the marbles in Box A were black and 3/4 of the marbles in Box B were black.a)How many black marbles were removed from Box B to be placed in Box A? Ans.:175b)How many white marbles were removed from Box B to be placed in Box A? Ans.:25

black

Box A

white

350

500

Box B

400

100

-?

-?

+?

+?

1u + 3p -->1u + 3p --> 7501u --> 750

1u + 1p -->1u + 1p --> 6001u --> 600

750

3p1u

1p1u

3p – 1p -->600 2p --> 150

1p --> 1503p --> 3 x

400 -100 -

(75)

(225)1u

1u

3p

1p

350 + 400

– 3p

500 + 100

– 1p

750 - 600

÷ 2 = 7575 = 225

225 = 175 (a)75 = 25 (b)

When Kok's age was twice as Bala's age, Mike's age was 30. When Mike's age was twice Kok's age, Bala's age was 21. Given that Mike was the oldest among the three persons, find Bala's age when Mike was 62 years old. Ans.:35

Kok‘s

Bala‘s

2u

1u

Mike‘s 30 2p

1p

211u 1u

1p

(1u +1u 21

2u + 1u --> 303u --> 91u --> 9 ÷

62

2u +

2u + 21 --> 2 x

(27)

62 –

21)

- 21

3 = 3

?21

3 + 21 = 2727 = 35 (ans.)

Jane and Iris has 255 sweets altogether. Jane had 15 more sweets than Iris. Jane gave away 25% as many sweets as Iris. She was left with twice as many sweets as Iris. a)How many sweets did Iris give away? Ans.:60b)How many sweets did Jane have in the end? Ans.:120

Jane

Iris

255 15

1/4

Iris: (255 – 15) ÷

120

Jane: 120 +

135 -1u

-4u

2p

1p

2p --> 135 1p --> 1202p --> 240

x2

240

8u2p

135

1u2p

8u – 1u -->7u --> 105

1u --> 105 ÷ 7 = 15Iris (gave):Jane (end): 135

2 = 120 15 = 135

– 1u – 4u– 8u

240 - 135

4u --> 4 x 15 = 60 (a)– 1u --> 135 – 15 = 120 (b)

If I buy 3 Oranges and 5 Apples, I will have $0.70 left. If I buy 4 oranges and 4 apples, I will need another $0.50. Given that an apple costs $0.80, find the amount of money I have. Ans.:$10.70

$4 $3.20

Total

3 OR$0.70

4 OR

$0.50$4

$3.20

4 OR – 3 OR -->1OR --> 2

Total: 3 OR +

4 + 0.70 + 0.50 – 3.20

4 + 0.70 --> 3 x 2 + 4.70 = $10.70 (ans.)