The area of a rectangle is given by the expression w x l, where w is its width and I is its length.
a Find the area if w = 5 and/ = 7.
b Find the area if w = 2 and/ = 10.
a) If w = 5 and l = 7, the area of the rectangle would be 5 x 7 = 35.
b) If w = 2 and l = 10, the area of the rectangle would be 2 x 10 = 20.
The perimeter of a square with width w is given by the expression 4w.
a Find the perimeter of a square with width 6 cm (i.e. w 6).
b Find the perimeter of a square with width 10 m (i.e. w = 10).
a) If the width of the square is 6 cm, then the perimeter would be 4w = 4(6) = 24 cm.
b) If the width of the square is 10 m, then the perimeter would be 4w = 4(10) = 40 m.
Consider the equilateral triangle shown.
a Write an expression that gives the perimeter of this triangle.
b Use your expression to find the perimeter if x = 12.
x
x
x
a) The perimeter of an equilateral triangle is given by the expression 3x, where x is the length of each side.
b) If x = 12, then the perimeter of the triangle would be 3x = 3(12) = 36.
A car travels at 60 km/h, so in n hours it has
travelled 60n kilometres.
a
b
C
How far does the car travel in 3 hours (i.e.
How far does the car travel in 30 minutes?
Write an expression for the total distance (in
km) travelled in n hours for a motorbike
with speed 70 km/h.
a) If the car travels at 60 km/h, in 3 hours it would travel 60n = 60(3) = 180 kilometers.
b) To find how far the car travels in 30 minutes, we need to convert the time from hours to minutes. Since there are 60 minutes in 1 hour, 30 minutes would be equal to 30/60 = 0.5 hours. Therefore, in 0.5 hours, the car would travel 60n = 60(0.5) = 30 kilometers.
c) The expression for the total distance (in km) traveled in n hours for a motorbike with a speed of 70 km/h would be 70n kilometers.
A carpenter charges a $40 call-out fee and then $80 per hour. This means the total cost,
in dollars, for x hours of work is 40 +
a How much would it cost for a 2-hour job (i.e. x = 2)?
b How much would it cost for a job that takes 8 hours?
C The call-out fee is increased to $50. What is the new' expression for the total cost,
in dollars, of x hours?
a) For a 2-hour job (x = 2), the total cost would be: 40 + 80(2) = 40 + 160 = $200.
b) For a job that takes 8 hours (x = 8), the total cost would be: 40 + 80(8) = 40 + 640 = $680.
c) If the call-out fee is increased to $50, the new expression for the total cost of x hours would be: 50 + 80x.
A plumber charges a $50 call-out fee and $100 per hour.
Copy and complete the table below.
Number of hours 1
2
3
4
Total costs (S)
5
b
C
Find the total cost if the plumber works for t hours.
Give an expression.
Substitute t = 30 into your expression to find how much it will cost for the plumber
to work 30 hours.