AC9M9M05Year 9MeasurementPractised in part

AC9M9M05 — Year 9 Measurement

Official Curriculum Content Description:

use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings

Coverage notice: Practised in part

What this practice covers: finding a value under direct proportion

What is omitted: formulating a proportion model, interpreting and evaluating it

Worked Examples (1)

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Example 1Direct Proportion Equations & Constants

Given that

y

is directly proportional to

x

, and

y = 72

when

x = 12

, find the value of

y

when

x = 10

Common mistake: Using additive reasoning (

y = x + 60

) instead of multiplicative scaling (

y = kx

Correct Answer:

60

Worked Solution:

1. Since

y \propto x

, write the equation

y = kx

. 2. Substitute

x = 12

and

y = 72

to find

k

k = 72 \div 12 = 6

. 3. Substitute

x = 10

into

y = 6x

y = 6 \times 10 = 60

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