At a hawker centre, each table has either 4 or 6 chairs around it.
The number of tables to the number of chairs is $8 : 36$.
What is the ratio of the number of tables with 6 chairs to that with 4 chairs?
(1) $2 : 1$
(2) $1 : 3$
(3) $3 : 1$
(4) $3 : 4$
(2)
Assume all 8 tables have 4 chairs:$$8 \times 4 = 32\text{ chairs}$$
Compare with the actual number of chairs:$$36 - 32 = 4\text{ extra chairs}$$
Each table changed from 4 to 6 chairs adds:$$6 - 4 = 2\text{ chairs}$$
Number of tables with 6 chairs:$$4 \div 2 = 2$$
Number of tables with 4 chairs:$$8 - 2 = 6$$
Check: $2 \times 6 + 6 \times 4 = 12 + 24 = 36\text{ chairs}$ ✓
Ratio of tables with 6 chairs to tables with 4 chairs:$$2 : 6 = 1 : 3$$
The answer is option (2).$$\boxed{1 : 3}$$
Average chairs per table$$\frac{36\text{ chairs}}{8\text{ tables}} = 4.5\text{ chairs/table}$$
Using weighted average / 'Alligator' method
Let $x$ be the number of tables with 4 chairs and $y$ be the number of tables with 6 chairs.
The average number of chairs per table is $4.5$.
The difference between the average and the 4-chair tables is $4.5 - 4 = 0.5$.
The difference between the 6-chair tables and the average is $6 - 4.5 = 1.5$.
The ratio of the number of tables with 6 chairs to the number of tables with 4 chairs is inversely proportional to these differences.$$y : x = 0.5 : 1.5$$
$$y : x = 1 : 3$$
The answer is option (2).
