Units & Parts Concept (Total of 2 Combos)

3 erasers and 2 pens cost $2.55. 1 eraser and 1 pen cost $1.05. Find the cost of 1 pen. 

Set 1 (Item 1) vs Set 2 (Item 2)
Amount (Total of 2 Combos)

First

5 toothbrushes and 2 toothpastes cost $27.15.
2 toothbrushes and 3 toothpastes cost $17.35.

a) What is the cost of one toothbrush?
b) What is the cost of one toothpaste?

5b + 2p = $27.15

10b + 4p = $54.30

2b + 3p = $17.35

10b + 15p = $86.75

15p -- 4p = 86.75 - 54.30
11p = $32.45
1 Toothpaste = 1p = $32.45 ÷ 11 = $2.95

2p = 2.95 × 2 = $5.90
5b + 2p = $27.15
5b = 27.15 -2p = 27.15 - 5.90 = $21.25
1 Toothbrush = 1b = 21.25 ÷ 5 = $4.25

Second
The cost of 2 mangoes and 5 apples is $5.00 altogether. The cost of 2 mangoes and 1 apple is $1.80. What is the cost of 1 apple?

Third
A puzzle book and 2 picture books cost $8.50. 1 puzzle book and 4 picture books cost $14.50. What is the cost of 1 puzzle book?

Fourth

Mrs Chan paid a total of $31 for 3 kg of sugar and 5 kg of rice. Mrs Wong bought 1 kg of sugar and 5 kg of rice for $27. What was the cost of 1 kg of rice?

4

Fifth
3 pairs of shorts and 7 belts cost $105. 3 pairs of shorts and 1 belt cost $33. What is the cost of 1 pair of shorts?

Sixth
The total cost of 2 mangoes and 5 apples is $5.00. The cost of 1 mango and 1 apple is $1.30. What is the cost of 1 apple?

Seventh
Mrs Chan Paid a total of $31 for 3 kg of sugar and 5 kg of rice. Mrs Wong bought 1 kg of sugar and 2 kg of rice for $12. What is the cost of 1 kg of rice?

Eighth
3 pairs of shorts and 7 belts cost $105. 2 pairs of shorts and 1 belt cost $26. What is the cost of 1 pair of shorts?

Ninth
3 puzzle books and 2 picture books cost $13.50. 1 puzzle book and 4 picture books cost $14.50. What is the cost of 1 puzzle book?

Tenth
Albert planned to buy 5 pencil cases and 6 books which cost $130 altogether. However, he changed his mind and bought 3 pencil cases and 7 books instead. He paid $146 for these items. How much did a book cost?

Eleventh
Family A paid $31 to watch a concert. Theg bought 2 adult tickets and 3 child tickets. Family B paid $34 for 3 adult tickets and 2 child tickets to watch the same concert. How much did an adult ticket cost?

Twelfth
Mrs Ho paid $23 for 2 kg of sugar and 5 kg of rice. Mrs Lee paid $39.50 for 5 kg of sugar and 8 kg of rice. Find the total cost of 3 kg of sugar and 3 kg of rice.

Thirteenth
Wendy used 149 beads to make 5 necklaces and 3 rings. If she used 17 less beads to make 4 necklaces and 4 rings, how many beads did she use make a necklace?

James bought 4 oranges, 3 pears and 3 apples for $4.50. The total cost of an orange and a pear was 95¢. The total cost of an orange and an apple was 85¢. Find the total cost of an apple and a pear. 

Units and Parts Concept (Pair and Total)

Set 1 (Item 1) vs Set 2 (Item 2)
Amount (Pair and Total)


First
There were 610 watches and pens in a box. 1/5 of the watches and 1/3 of the pens were made in Switzerland. The rest were made in Germany. A total of 150 watches and pens were made in Switzerland. How many watches were there in the box?

(Watches)
Switzerland : Germany : Total
= 1u : 4u:  5u


(Pens)
Switzerland : Germany : Total
= 1p : 2p : 3p

(Total)
5u + 3p = 610

(Switzerland)
1u + 1p = 150
3u + 3p = 450

2u = 160
Watches = 5u = 400

Second
There were 205 cakes and pies in a shop. 1/2 of the pies were strawberry pies and 1/3 of the cakes were strawberry cakes. The rest were blueberry pies and cakes. There were 80 strawberry cakes and pies. How many cakes were there altogether?

(Pies)
Strawberry : Blueberry : Total
= 1u : 1u : 2u


(Cakes)
Strawberry : Blueberry : Total
= 1p : 2p : 3p

(Total)
2u + 3p = 205

(Strawberry)
1u + 1p = 80
2u + 2p = 160

1p = 45
Cakes = 3p = 135

Third
There were 290 adults and children at a party. 1/7 of the adults and 1/5 of the children were males while the rest were females. If there were 50 males, how many children were there at the party?


(Adults)
Males : Females : Total
= 1u : 6u : 7u


(Children)
Males : Females : Total
= 1p : 4p : 5p


(Total)
7u + 5p = 290


(Males)
1u + 1p = 50
7u + 7p = 350

2p = 350 - 290 = 60
Children = 5p = 150


Fourth
There were 61 pupils in a robotics class. 8/9 of the boys and 4/5 of the girls were Singaporeans. The rest were foreigners. If there were 52 Singaporeans, how many Singaporean boys were there in the robotics class?


(Boys)
Singaporeans : Foreigners : Total
= 8u : 1u : 9u


(Girls)
Singaporeans : Foreigners : Total
= 4p : 1p : 5p


(Total)
9u + 5p = 61


(Foreigners)
1u + 1p = 61 - 52 = 9
5u + 5p = 45


4u = 61 - 45 = 16
Singaporean Boys = 8u = 32


Fifth
There were a total of 186 local and foreign stamps. After 1/2 of the local stamps and 1/3 of the foreign stamps were sold, there were 109 stamps left.

a) How many foreign stamps were sold?
b) How many local stamps were left?


(Local Stamps)
Sold : Left : Total
= 1u : 1u : 2u


(Foreign Stamps)
Sold : Left : Total
= 1p : 2p : 3p


(Total)
2u + 3p = 186


(Sold)
1u + 1p = 186 - 109 = 77
2u + 2p = 154


1p = 186 - 154 = 32
Foreign Stamps Sold = 1p = 32


Local Stamps Left = 1u = 77 - 1p = 77 - 32 = 45

Sixth

There are 36 pupils in a class. 7/8 of the boys and 3/4 of the girls can swim. There are 29 pupils in the class who can swim. 

a) How many boys are there in the class? 

b) How many girls can swim? 

Units & Parts Concept (Proportional Change)

Set 1 (Before) vs Set 2 (Proportional Change)
Amount (After)

First
Mrs Kumar bought 2/3 as many chocolate muffins as blueberry muffins.
After she packed 3 chocolate muffins and 5 blueberry muffins into each box, she had 13 chocolate and 11 blueberry muffins left.
How many chocolate muffins did Mrs Kumar buy?

(Before)
Chocolate : Blueberry
= 2u : 3u

(Change)
Chocolate: Blueberry
= 3p : 5p

(Chocolate)
2u - 3p = 13
6u - 9p = 39

(Blueberry)
3u - 5p = 11
6u - 10p = 22

-9p - (-10p) = 39 - 22
1p = 17

Chocolate (Before)
= 2u
= 3p + 13
= 3 (17) + 13 = 64

Set 1 (Before), Set 2 (Proportional Change)
Amount (2 changes)

First
A box contains red marbles and white marbles. 80% of the marbles in the box are red marbles. 28 red marbles and 2 white marbles are removed from the box and the remaining marbles are put into groups of 9 marbles. In each group of 9 marbles, there are 7 red marbles. Find the number of marbles in the box at first.

Second
Mr Tan baked some mooncakes. There were 25% fewer pandan mooncakes than lotus paste mooncakes. He took 20 pandan mooncakes to give to his friends and baked another 13 lotus paste mooncakes. He packed the rest into boxes of 7 mooncakes each. If there were 5 lotus paste mooncakes in each box, how many pandan mooncakes did he bake at first?

Third
In the morning, Smith baked 2/3 as many vegetable pies as curry pies. At noon, he baked 18 vegetable pies and 15 curry pies. After that Smith packed the pies into boxes of 9. In each box, 4 of the pies were vegetable pies. Find the number of vegetable pies Smith baked in the morning.

Fourth
Gareth had 40% as many red shirts as blue shirts at first. He bought  another 80 red shirts and said away 70 blue shirts. He packed the remaining shirts into packs of 11. In each pack. there were 7 red shirt and 4 blue shirts. How many shirts did Gareth have at first?

Units & Parts Concept (Change by a Ratio)

Set 1 (Before)
Set 2 (Change)
Amount (2 Sides)

First
James had $2900 and Rose had $1000 at first. After James had bought a laptop that cost twice as much as the laptop Rose bought, James has 5 times as much money left as Rose. How much did Rose's laptop cost?

(Before)
James : Rose
= $2900 : $1000

(Change)
James : Rose
= 2u : 1u

(After)
James : Rose
= 5p : 1p

(James)
$2900 - 2u = 5p

(Rose)
$1000 - 1u = 1p
$5000 - 5u = 5p

5000 - 2900 -5u -(-2u) = 0
2100 - 3u = 0
3u = 2100
Cost of Rose's Laptop = 1u = $700

Second
Carl had $400 and Ester had $120 at first. The book Carl bought cost $30 more than twice the book Ester bought. Carl now has four times as much money left as Esther has left. How much did Carl pay for his book?


(Before)
Carl : Esther
= $400 : $120

(Change)
Carl : Esther
= (2u + $30) : 1u

(After)
Carl : Esther
= 4p : 1p

(Carl)
400 - 2u - 30 = 4p
370 - 2u = 4p

(Esther)
120 - 1u = 1p
480 - 4u = 4p

480 - 370 -4u - (-2u) = 0
110 - 2u = 0
2u = 110

Amount Carl Paid = 2u + $30 = 110 + 30 = $140

Third

Units and Parts Concept (2 Changes + Money Substitution)

First
The number of ten-cent coins in a box was 1/2 the number of fifty-cent coins. Syed took out 5 fifty-cent coins and exchanged them for ten-cent coins. Then he put the money back into the box. The number of fifty-cent coins became 5/8 the number of ten-cent coins. How much money was there in the box?

(Before)

10 cents : 50 cents

= 1u : 2u

(After)

10 cents : 50 cents

= 8p : 5p

(Change)

1 × 50 cent coins = 5 × 10 cent coins

loss of 5 × 50 cent coins = gain of 25 × 10 cent coins

(50 cent coins) 

2u - 5 = 5p

(10 cent coins)

1u + 25 = 8p

Second
In a bag, the ratio of the number of $2 notes to the number of $10 notes were 3 : 4. Ten $10 notes were removed from the bag to exchange for $2 notes which were then put back into the bag. The total value of money in the bag was unchanged after the exchange. The ratio of the number of $2 notes to the number of $10 notes then became 8 : 3. Find the ratio of the value of the $2 notes to the value of the $10 notes in the bag after the exchange. Leave your answer in its simplest form.

Third

A box contained 50-cent and 20-cent coins in the ratio 2:3.

Some 50-cent coins were taken out and exchanged for 20-cent coins.
The ratio of the number of 50-cent coins to the number of 20-cent coins became 2:7. Find:

a) the total value of money in the box
b) the number of 50-cent coins which were taken to exchange for 20-cent coins.

2 x 0.50 coin = 5 x 0.20 coin

Total Value = $0.50 × 2 units + $0.20 × 3 units = $1.00u + $0.60u = $1.60u

Total Value = $0.50 × 2 parts + $0.20 × 7 parts = $1.00p + $1.40p = $2.40p

1.60u = 2.40p

2u = 3p

3u = 4.5p

0.50 x 3p + 0.20 x 4.5p = 1.5p + 0.6p

Units & Parts Concept (2 Changes)

Set 1 (Before) vs Set 2 (After)
Amount (2 Changes)


First

Felicia collected 1/5 as many seashells as Gareth at the beach at first. Then, Felicia found 5 more seashells and Gareth found 12 more seashells. The ratio of the number of seashells Gareth had to the number of seashells Felicia had became 4 : 1. How many seashells did Gareth have at first?

(Before)
Felicia : Gareth
= 1u : 5u


(Change)
Felicia >> +5
Gareth >> +12

(After)
Felicia : Gareth
= 1p : 4p

Approach 1:
Equalise and Eliminate the Parts

(Felicia)
1u + 5 = 1p
4u + 20 = 4p

(Gareth)
5u + 12 = 4p

1u - 8 = 0
1u = 8

Gareth (Before) = 5u = 40

Approach 2:
Equalise and Eliminate the Units

(Felicia)
1u + 5 = 1p
5u + 25 = 5p

(Gareth)
5u + 12 = 4p

13 = 1p
5p = 65

Gareth (Before) = 5p - 25 = 65 - 25 = 40


Second 

Jane had 2/5 as many kiwi fruits as Bernice at first. Jane bought another 8 kiwi fruits and Bernice ate 5 kiwi fruits.  Then, Jane had 4/5 as many kiwi fruits as Bernice. Find the number of kiwi fruits Jane had at first.

(Before)
Jane : Bernice
= 2u : 5u


(Change)
Jane >> +8
Bernice >> -5

(After)
Jane : Bernice
= 4p : 5p

Approach 1:
Equalise and Eliminate Parts

(Jane)
2u + 8 = 4p
10u + 40 = 20p

(Bernice)
5u - 5 = 5p
20u - 20 = 20p

10u - 20 - 40 = 0
10u - 60 = 0
10u = 60

Jane (Before) = 2u = 12

Approach 2:
Equalise and Eliminate the Units

(Jane)
2u + 8 = 4p
10u + 40 = 20p

(Bernice)
5u - 5 = 5p
10u - 10 = 10p

40 - (-10) = 10p
10p = 50
4p = 20

Jane (Before) = 2u = 4p - 8 = 20 - 8 = 12

Third
At a pet shop, the number of puppies was 1/2 of the number of kittens at first. After 80 kittens and 12 puppies were sold, the number of kittens left was 2/5 of the number of puppies left. What was the total number of puppies and kittens in the pet shop at first?


Fourth
The number of spoons and forks in a restaurant was 3 : 7 respectively. After the chef bought 6 more spoons and 4 more forks, the number of spoons became 1/2 of the number of forks. How many forks did the chef have after the purchase?


Fifth

The ratio of the number of boys to the number of girls on a club last year was 2 : 3. This year, 44 boys joined the club and 12 girls left. The ratio of the number of boys to the number of girls becomes 5 : 1. How many members are there in the club this year?

Sixth

Rosa had 0.75 of the amount Clement had. When he spent $372 and she spent $124, she would have twice as much as the amount he had left. How much did each person have at first?

3u - 124 = 2p

4u - 372 = 1p

8u - 744 = 2p

5u - 744 + 124 = 0

5u = 620

1u = 124

3u = 373

4u = 496