Chapter 38: Direct Proportion

✏️ Explanation

In direct proportion, as one quantity increases, another increases at the same rate. If y is directly proportional to x, then y = kx.

Many real-world relationships follow direct proportion: speed and distance, ingredients in recipes, wages and hours.

🧭 See chart: "Direct Proportion Solver" (to be added)

If 5 apples cost £2, how much do 8 apples cost?

Step 1: Find the cost per apple

Cost per apple = £2 ÷ 5 = £0.40

Step 2: Calculate cost for 8 apples

8 apples cost 8 × £0.40 = £3.20

items cost £

How much do items cost?

Result:

£3.20

Working: 8 × £0.40 = £3.20

1. 3 pens cost £4.50. Find the cost of 7 pens.

Cost of 7 pens: £

2. If y is proportional to x, and y = 15 when x = 3, find y when x = 7.

y =

3. 4 hours of work earns £32. How much for 9 hours?

Earnings for 9 hours: £

4. 6 litres of petrol costs £8.40. Find cost of 10 litres.

Cost of 10 litres: £

5. Recipe for 4 people uses 200g flour. How much for 6 people?

Flour needed: g

Direct proportion: as one goes up, the other goes up proportionally. Find the rate first.