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)

Speed Concepts (Divergence)

Given: Diverging Distance, Diverging Time, One Speed
Answer: Other Speed

First
Mr Lee and Mr Tan started driving from Point A in opposite directions. After driving for 4 hours, they were 660 km apart. If Mr Lee's driving speed was 100 km/h, find Mr Tan's average driving speed.


Given: Diverging Time, 2 Speeds
Answer: Diverging Distance


First
Timothy and Jane started jogging from the same place at the same time but in opposite directions along a straight road. Timothy's speed was 10km/h while Jane's speed was 8km/h. After jogging for 3 hours, how far apart were they?

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Total Speed = 10km/h + 8km/h
= 18km/h

Total Distance = 18km/h × 3h = 54km

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Given: Difference in Speed, Diverging Distance, Common Time
Answer: Fast or Slow Speed

First
Kerrine and Thompson started walking from the same starting point, but in opposite directions along a straight path.
Kerrine's average speed was 4 km/h more than Thomson's.
After walking for 3 hours, they were 40 km apart.
What was Kerrine's average walking speed.


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Difference in Distance = 4 km/h x 3 h = 12 km


Kerrine's Distance  = (40km + 12km) / 2 = 26 km


Kerrine's Speed = 26 km / 3 h = 8 2/3 km/h

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Second
Andy and Candy left their house at the same time and travelled in opposite directions.

Candy drove at a speed of 16km/h slower than Andy.
30 minutes later, Andy arrived at his destination, while Candy stopped for a rest.
They were 100km apart then.
Find Andy's speed.

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Difference in Distance = 16 km/h x 1/2 h = 8 km


Andy's Distance = (100 km + 8 km) / 2 = 54 km


Andy's Speed = 54 km / 1/2 h = 108 km/h

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