Variables and formulas

Letters that stand for numbers

In Aussie Rules, a goal is worth 6 points and a behind is worth 1. A team's score is:

S = 6g + b

S, g and b are variables: letters that stand for numbers that can change (the score, the goals, the behinds). A rule like this is a formula. In algebra, 6g means 6 × g.

Substituting

To use a formula, substitute (swap in) the numbers you know:

Worked example: a footy score

1. A team kicks 12 goals and 9 behinds (written 12.9).
2. S = 6 × 12 + 9
3. S = 72 + 9 = 81 points

Changing the variables

A party venue charges $40 plus $15 per person: C = 15n + 40. A spreadsheet can show what happens as n changes. Type the numbers of people in column A, and in B2 type =15*A2+40, then fill down:

Each extra person adds exactly $15 — the number in front of n. The $40 is the starting cost even with nobody there. Spotting how a formula behaves when you change one variable is a powerful skill.

Your turn

Use a pencil and paper. The answers are at the bottom of the page — try first!

1. Use S = 6g + b for a score of 9 goals 14 behinds.
2. Use P = 2l + 2w with l = 12 and w = 5.
3. Use A = l × w with l = 7.5 and w = 4.
4. Use C = 15n + 40 for 24 people.
5. Use F = 1.8C + 32 to change 100 °C to °F.
6. In C = 15n + 40, what happens to C when n goes up by 2?

Answers

1. 6 × 9 + 14 = 68 points
2. 24 + 10 = 34
3. 30
4. 15 × 24 + 40 = 360 + 40 = $400
5. 180 + 32 = 212 °F
6. C goes up by 2 × 15 = $30

For parents and teachers — this lesson covers the Victorian Curriculum Mathematics Version 2.0, Level 7:

• VC2M7A01: recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown
• VC2M7A06: manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables