# Bar Model Method with Distributive Law For Chicken-Rabbit Approach

##### Ho Soo Thong

**Abstract**

This article illustrates a bar modelling problem solving approach to a classical chicken-rabbit problem which involves distributive property situations.

## 1. A Classic Chickens-Rabbits Problem

The following classic word problem , chickens and rabbits in a cage, posed in the ancient Chinese book* Sunzi Suanjing* :

*There are chickens and rabbits in a cage.**Look at the top of the cage – there are 35 heads.**Look at the bottom of the cage – there are 94 legs.**How many chickens and how many rabbits are there in the cage?*

The problem involves the *Actual *situation:

There are 35 chickens and rabbits and there is a total of 94 legs

where each rabbit has 4 legs and each chicken has 2 legs.

The strategy here is to add the *Supposed *situation :

There are 35 chickens and therefore a total of 35×2 = 70 legs.

Figure 1 shows the bar models for the number of chickens and rabbits and the corresponding bar model for the number of legs.

Therefore we have 23 chickens and 12 rabbits.

## 2. Variants of Chicken-Rabbit Problems

Now, we simplify the presentation in the same approach to a counting problem.

### Example 1

There is a total of 33 triangles and squares, and they have a total of 113 vertices.

How many triangles and how many squares are there?

### Solution

Figure 2 shows the bar model for number of vertices in the *Actual *situation and the *Supposed *situation in which we suppose that the shapes are triangles. A square has 4 vertices and a triangle has 3 vertices.

Therefore, there are 19 triangles and 14 squares.

Next, we apply the Chickens-Rabbits problem solving problem to a simple finance problem.

### Example 2

Jennifer spent $ 24.80 for a total of 30 apples and oranges.

An apple costs 70₡ and an orange costs 90₡.

How many apples and how many oranges did Jennifer buy?

### Solution

Figure 3 shows the bar model for the amounts spent in the *Actual *situation and the *Supposed *situation in which we suppose that only apples are bought. *An orange costs 20¢ more than an apple.*

Therefore, Jennifer bought 11 apples and 19 oranges

**3. A Challenging Problem**

Finally, we post a complex problem which requires the chicken-rabbit problem solving approach to be applied twice.

*A total of 31 teachers and students plan for a two-nights excursion.**Teachers prepare 96 kg of food and 43 kg of camping equipment.**Each teacher will carry 4 kg of food. Among the students, each boy will carry 3 kg of food together with 2 kg of equipment and each girl will carry 3 kg of food together with 1 kg of equipment.**How many boys and how many girls are there in the excursion?*

References

[1] Ho Soo Thong, Ho Shuyuan, Bar Model Method for PSLE and Beyond – AceMath, 2011

[2] Ho Soo Thong, Ho Shuyuan and Leong Yu Kiang Problem Solving methods for Primary Olympiad Mathematics, AceMath, 2012.