Applying algebra

Writing algebraic expressions and rules for real situations such as costs, perimeters and patterns, and using them to answer questions.

Writing a model

Example 1●

A plumber charges a $\$60$ call-out fee plus $\$45$ per hour. Write an expression for the cost of $h$ hours, and find the cost of a $3$-hour job.

Cost $= 60 + 45h$ dollars.

When $h = 3$: $60 + 135 = \$195$.

Matchstick squares in a row use $4, 7, 10, 13, \ldots$ matches. Each new square adds $3$ matches.

Matchstick pattern

Drag the point. The number of matches goes up by 3 for each extra square.

Example 2●●

How many matches are needed for $50$ squares?

$3 \times 50 + 1 = 151$

Flashcards

Fixed fee + rate

Cost $=$ fee $+$ rate $\times$ amount

Pattern 5, 9, 13, ...

Rule $4n + 1$

Check a rule

Substitute $n = 1$ and compare.

Practice

Cost $= 60 + 45h$. Find the cost for $h = 3$.
Matches $= 3n + 1$. How many for $50$ squares?
The rule for $5, 9, 13, 17, \ldots$ is:
Tickets cost $\$12$ each plus a $\$5$ booking fee. The cost of $t$ tickets is:
Using cost $= 12t + 5$, find the cost of $5$ tickets.
A square has side $s$. Its perimeter is:
For the rule $2n - 1$, what is the difference between consecutive terms?
Sam is $x$ years old and Mia is $x + 3$. Find the sum of their ages when $x = 16$.