# 3.02 Problem solving with linear equations

## Interactive practice questions

Matches were used to make the pattern attached:

a

Complete the table:

 Number of triangles ($t$t) Number of matches ($m$m) $1$1 $2$2 $3$3 $5$5 $10$10 $20$20 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Write an equation that describes the relationship between the number of matches ($m$m) and the number of triangles ($t$t).

c

How many matches are required to make $21$21 triangles using this pattern?

Easy
Approx 2 minutes

A diver starts at the surface of the water and starts to descend below the surface at a constant rate. The table shows the depth of the diver over $5$5 minutes.

There are $40$40 litres of water in a rainwater tank. It rains for a period of 24 hours and during this time, the tank fills up at a rate of $10$10 Litres per hour.

Consider the points in the table. The time $($($x$x$)$) is measured in minutes.

### Outcomes

#### VCMNA335

Solve problems involving linear equations, including those derived from formulas.