Elimination Concept (Container and Content)

First
When 3/5 of a container is filled with sand, the total mass of the container is 13.5kg. When 1/4 is filled with sand, the total mass of the container is 6.5kg. What is the mass of the empty container?

(Case 1)
3/5 = 12/20

Container + 12u = 13.5kg

(Case 2)
1/4 = 5/20

Container + 5u = 6.5kg

7u = 7.0kg

Approach 1: Using Case 1

5u = 5.0kg
Container = 6.5kg - 5u
= 6.5 - 5.0 = 1.5kg

Approach 2: Using Case 2

12u = 12.0kg
Container = 13.5kg - 12u
= 13.5 - 12.0 = 1.5kg

Second
The mass of a rice cooker is 3.3kg when 2/3 of it is filled with rice and water. The mass of the same rice cooker is 2.74kg when it is 1/5 filled with rice and water. What is the mass of the rice cooker when it is empty?

(Case 1)
2/3 = 10/15

Container + 10u = 3.3kg

(Case 2)
1/5 = 3/15

Container + 3u = 2.74kg

7u = 0.56kg

Approach 1: Using Case 1

Container = 2.74 - 3u
= 2.74 - 0.24 = 2.5kg

Approach 2: Using Case 2

Container = 3.3kg - 10u
= 3.3 - 0.8 = 2.5kg

Third
When 1/3 of a paper box is filled with sand, its mass is 130g. When 3/4 of the box is filled with sand, its mass is 230g. What is the mass of the box when it is empty?

(Case 1)
1/3 = 4/12
Container + 4 units = 130g


(Case 2)
3/4 = 9/12
Container + 9 units = 230g


5 units = 100g
4 units = 80g

Container = 130g - 80g = 50g

Fourth
The mass of a tank that is 2/5 filled with water is 4.4kg. The mass of the same tank is 6.5kg when it is 3/4 filled with water. What is the mass of the tank when it is empty?


Case 1
2/5 = 8/20
Container + 8 units = 4.4kg

Case 2
3/4 = 15/20
Container + 15 units = 6.5kg

7 units = 2.1kg
8 units = 2.4kg


Container = 4.4kg - 2.4kg = 2.0kg

Fifth
The mass of a container with 50 identical metal balls is 750 g.
When 20 of the balls were removed, the mass of the container with the remaining balls is 510 g.
What is the mass of each metal ball?

Sixth

A metal tin had a mass of 4.6 kg when it was half filled with iron nails. When it was 5/6 full, its total mass was 5.8 kg. Find the actual mass of the iron nails when it was 5/6 full. 

Elimination Concept (3 Totals + 3 Variables)

First
Bags A, B, and C have candies inside them.
Bag A and Bag B have 69 candies.
Bag B and Bag C have 84 candies.
Bag C and Bag A have 79 candies.
a) How many candies are there in Bag C?
b) How many candies are there altogether?

Answer: (A: 32, B: 37, C: 47, Altogether 116)

Second
There are three candidates in a small town election: Obama, Mitt, and Donald.
Obama obviously won by a landslide. The votes were counted and it was revealed that Obama and Mitt won 1077 votes together, Mitt and Donald won 310 vote while Donald and Obama won 805 votes.

a) How many votes did Donald Trump win?
b) How many voters were there in that small town?

Answer: (Obama: 786, Mitt: 291, Donald: 19, Voters: 1096)

Third
There were three categories that contestants in a singing competition could compete in: Student, Adult and Group categories. Each contestant can only compete in only one category. There were 444 contestants in the Student and Adult categories.
On the other hand, there were 292 for the Student and Group categories.
For the Adult and Group categories, there were 308 entries.

a) How many students competed in the singing competition?
b) How many contestants were there in all?

Fourth
There are three classrooms in front of you.
The first and the second classrooms contain 59 students.
The second and the third classrooms contain 53 students.
The third and the first classrooms contain 50 students.
a) How many students are there in the second classroom?
b) How many students are there in the three classrooms altogether?

Answer: (A: 28, B: 31, C: 22, Altogether: 81)