# Understand Direct Proportion Using Indices

In this worksheet, students will be asked to resolve problems related to direct proportion with indices.

Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Solve Problems Involving Direct and Inverse Proportion

Difficulty level:

#### Worksheet Overview

Direct proportion refers to the relationship between two variables where their ratio is equal to a constant value.

We call this the multiplier when exchanging currency, for example.

Example

Given that y is directly proportional to x and that x = 19 when y = 133.

Find:
(i) a formula connecting y and x
(ii) the value of y when x = 13
(iii) the value of x when y = 119

y ∝ x

So, y = kx for a constant k.

(i) Given x = 19, when y = 133,

133 = k x 19

k = 133 ÷ 19 = 7

Therefore, the formula is y = 7x

(ii) When x = 13, y = 7 x 13 = 91

(iii) When y = 119, x = 119 ÷ 7 = 17

It's useful to have paper and a pencil in order to record your own workings.

These are not the kind of questions you can calculate mentally.

You can look back at this introduction at any point by clicking on the red help button on the screen.

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