4. The Chicken and Rabbit Problem

A farmer has 30 chickens and rabbits altogether. There are only 100 legs. Find the number of chickens and the number ofrabbits that the farmer has.

Chicken: Rabbit:

(a)  

Answer explanation

Samantha has 30 pieces of $2 and $5 notes altogether. The total value of the money she has is $120. Find the number of pieces of $2 notes and the number of pieces of

$5 notes that Samantha has.

$2: $5:

(a)  

Answer explanation

Alternative Assumption

If we assume all were $2 notes,

30 × $2 = $60

the total value would be $60.

$120 - $60 = $60

There is a difference of $60 in the total value of money.

$5-$2= $3

$60÷$3= 20

Samantha has 20 pieces of $5 notes.

30- 20=10

Samantha has 10 pieces o f $2 notes.

There are 24 cars and motorcycles in a car park. There are a total of 76 wheels. How many motorcycles are there? How many cars are there?

cars: motorcycles:

(a)  

Answer explanation

There are 10 motorcycles.

24 - 10 = 14

There are 14 cars.

Alternative Assumption

If we assume all were motorcycles,

24x2=48

the total number of wheels would be 48.

76-48= 28

There is a difference of 28 in the total number of wheels.

4 -2=2

28÷2= 14

There are 14 cars.

24- 14= 10

There are 10 motorcycles.

There were 6 questions in a mathematics competition. 5 marks would be awarded for every correct answer. 2 marks would be deducted for a wrong answer. If Valerie

scored 23 marks in the mathematics competition, how many questions did she answer correctly?

(a)  

Answer explanation

There were 25 questions in amathematics quiz. Ifaquestion was answered correctly, 4 marks would be given, otherwise 1 mark would be deducted. If John scored 85 marks in the mathematics quiz, how many questions had he answered correctly?

(a)  

Answer explanation

There were a total of 30 cars and motorcycles at a car park. There were 100 wheels in all. How many

cars were there at the car park?

(a)  

Answer explanation

Each adult movie ticket costs $8. Each child movie ticket costs $5. Sean buys 10

movie tickets altogether. He pays $74 in al. Find the number of adult movie tickets and the number of child movie tickets Sean buys.

Adult: Child:

(a)  

Answer explanation

Clifford has 30 pieces of 50¢ and 20¢ stamps. The total value of all his stamps is $12. Find the number of 50¢ and 20¢ stamps Clifford has.

¢50: ¢20:

(a)  

Answer explanation

A spider has 8 legs and a dragonfly has 6 legs. There are 20 spiders and dragonflies altogether. There are 144 legs in al. Find the number of spiders and the number of dragonflies.

Spider: Dragonfly:

(a)  

Answer explanation

Natalie saves 30 pieces of $5 and $10 notes. Her total savings is $220. How many pieces of $10 notes does Natalie save?

(a)  

Answer explanation