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.
"Copy and complete the table below:
Number of hours | Total costs (S)
1 |
2 |
3 |
4 |
To find the total cost for each number of hours, we need to add the call-out fee of $50 to the cost per hour, which is $100 multiplied by the number of hours.
a) For 1 hour of work, the total cost would be: 50 + 100(1) = $150.
b) For 2 hours of work, the total cost would be: 50 + 100(2) = $250.
c) For 3 hours of work, the total cost would be: 50 + 100(3) = $350.
d) For 4 hours of work, the total cost would be: 50 + 100(4) = $450.
To find the total cost if the plumber works for t hours, the expression would be: S = 50 + 100t.
Substituting t = 30 into the expression S = 50 + 100t, the total cost for the plumber to work 30 hours would be: S = 50 + 100(30) = $3050."
Adrian's mobile phone costs 30 cents to make a connection, plus 60 cents per minute of talking.
This means that a t-minute call costs 30 + 60t cents.
a What is the cost of a I-minute call?
b What is the cost of a 10-minute call'? Give your answer in dollars.
C Write an expression for the cost of a I-minute call in dollars.
a) The cost of a 1-minute call would be 30 + 60(1) = 30 + 60 = 90 cents.
b) The cost of a 10-minute call would be 30 + 60(10) = 30 + 600 = 630 cents. To convert this to dollars, we divide by 100: 630/100 = $6.30.
c) The expression for the cost of a 1-minute call in dollars would be (30 + 60t)/100, where t is the number of minutes.
Hiring a basketball court costs SIO for a booking fee, plus $30 per hour.
a
b
C
d
e
Write an expression for the total cost in dollars to hire the court for x hours.
For the cost of $40, you could hire the court for I hour. How long could you hire the court
for the cost of S80?
Explain why it is not the case that hiring the court for twice as long costs twice as much.
Find the average cost per hour if the court is hired for a 5 hour basketball tournament.
Describe what would happen to the average cost per hour if the court is hired for many hours
(e.g. more than 50 hours).
a) The expression for the total cost in dollars to hire the court for x hours would be: SIO + 30x.
b) For the cost of $40, you could hire the court for 1 hour because the booking fee is included in the total cost.
c) To find out how long you could hire the court for the cost of $80, we need to subtract the booking fee from $80 and then divide the remaining amount by $30.
($80 - $10) / $30 = $70 / $30 = 2.33 hours
Therefore, you could hire the court for approximately 2.33 hours for the cost of $80.
d) Hiring the court for twice as long does not cost twice as much because there is a fixed booking fee of $10. So regardless of the length of time booked, you will always have to pay the booking fee, which remains constant.
e) If the court is hired for a 5-hour basketball tournament, the average cost per hour can be found by dividing the total cost by the number of hours.
Average cost per hour = (SIO + 30(5)) / 5 = (SIO + 150) / 5.
If the court is hired for many hours (e.g. more than 50 hours), the average cost per hour would decrease. This is because the booking fee of $10 gets distributed over a larger number of hours, reducing the average cost per hour.