3. Worked Examples

Worked Example 1: Scaling a Ratio

A recipe uses 3 cups of flour and 2 cups of milk (3:2). If you need 4 times the quantity, what is the new ratio?

• Multiply both values by 4:
• $3 \times 4 = 12, 2×4=8$ → Ratio is 12:8
• Answer: The ratio remains the same (3:2), just scaled up.

Worked Example 2: Simplifying Ratios

80 learners travel by bus, and 120 by taxi. What is the ratio in simplest form?

• 80:120 → Divide by 10 → 8:12 → Divide by 4 → 2:3
• Answer: 2:3

Worked Example 3: Ratios with Three Quantities

A grandmother shares R800 among 3 grandchildren in a ratio of 4:3:1. How much does each child get?

• Total parts = 4 + 3 + 1 = 8
• Shares:
• $\frac{4}{8} \times 800 = R400$
• $\frac{3}{8} \times 800 = R300$
• $\frac{1}{8} \times 800 = R100$
• Answer: R400, R300, R100

Worked Example 4: Unit Ratios

A hospital has 23 nurses and 7 567 patients. How many patients does each nurse care for?

• 23:7 567 → Divide by 23
• Answer: Each nurse cares for about 329 patients.

Worked Example 5: Solving a Proportion

Sipho arranges roses and daisies in a 1:3 ratio. He has 15 daisies. How many roses should he use?

• Set up proportion: $\frac{1}{3} = \frac{x}{15}$
• Cross-multiply: $3x = 15$
• Solve for x: $x = 5$
• Answer: Sipho should use 5 roses.

Worked Example 6: Proportion with Missing Number

A summer camp has a boy-to-girl ratio of 8:11. If the camp has 88 boys, what is the total number of children?

• Set up proportion**:** $\frac{8}{11} = \frac{88}{x}$
• Cross-multiply: $8x = 88 \times 11$
• Solve: $x = 121$
• Total children = 88 + 121 = 209
• Answer: 209 children

Worked Example 7: Using Rate Formula

A car travels at 60 km/h. How far does it travel in 3 hours?

• Distance = Speed × Time
• Distance = 60 × 3 = 180 km
• Answer: 180 km