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?