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.)