# Direct Proportion

**Direct proportion** is when **two quantities change in the same way**.

If you can multiply the first quantity by the same number (called a **constant**) to get the second quantity, they are in direct proportion.

For example, if 1 ice-cream costs $2, then 2 ice-creams will cost $4, 3 ice-creams cost $6, 4 ice-creams cost $8 and so on. You can multiply the number of ice-creams by 2 to get the cost of the ice-creams, so the number of ice-creams and the cost of ice-creams must be in direct proportion.

Other examples of direct proportion are:

**the cost of apples at $5 per kilogram****total wages earned at $20 per hour****amount of flour needed to make muffins**(at 3 cups of flour for every 10 muffins)**distance travelled and fuel used**(assuming the car speed is the same).

## Example One - Travel

A car travels 100 km in 1 hour. How far will it travel in 3 hours?

**Answer:**

The multiplying constant is 100.

3 × 100 = 300 km

## Example Two - Concrete

Four bags of cement are needed to make 1 cubic metre of concrete. How many bags are needed to make 5 cubic metres of concrete?

**Answer:**

The multiplying constant is 4.

5 × 4 = 20 bags

## Example Three - Medication

A sick child whose mass is 14 kg should receive medication dose that is in proportion to the dose of a 70 kg adult. If the adult dose is 10ml, how much should the child receive?

**Answer:**

The multiplying constant is 70 ÷ 14 = 5.

10 ÷ 5 = 2 ml.

## Questions

**Q1.** In adult cod fish who are constantly consuming seawater as they swim, their kidneys make **urine** at a constant rate of 50 millilitres every hour. How much urine does a cod fish make and excrete into the ocean in 5 hours?

**Q2.** Malik, a talented muffin maker, uses 2 cups of blueberries in every batch of **muffins**. How many cups of blueberries does he use when he bakes 6 batches?

**Q3.** My computer can download 100 **MP3 tracks** in 2 hours, how many can it download in 8 hours? (Hint: Find the multiplying constant, that is, the number of MP3s downloaded in 1 hour.)

**Q4.** A sick child whose mass is 28 kg receives a proportional **dose** to a 70 kg adult's dose of 100ml. What is the child's dosage?

**Q5.** In 1998, Australian Olympic gold medallist won the 200 metres **freestyle** in 1 minute 46.7 seconds and then the 400 metres freestyle in 3 minutes 44.35 seconds. Are these in direct proportion? (Hint: Work out the time for swimming 100 metres in each race.)

**Answers**
**A1.** 250 ml
**A2.** 12
**A3.** 400
**A4.** 40 ml
**A5.** No

## Did You Know That...?

**Caffeine**, found in coffee, tea, soft drinks and "energy drinks", can be **fatal** in large doses. One must consume 80 to 100 cups in a short time period.
Its effect is proportional to a person's mass. One can also suffer unhealthy symptoms from too much caffeine.