A charity calculates its total donations every month.
Over a six month period, the amounts they calculate are as follows:
$1520, $1270, $1600, $1310, $1430, $1288
What is the mean monthly donation the charity received over this 6 month period?
Aussie Maths Teachers: Save your time with SmarterMaths
A charity calculates its total donations every month.
Over a six month period, the amounts they calculate are as follows:
$1520, $1270, $1600, $1310, $1430, $1288
What is the mean monthly donation the charity received over this 6 month period?
`$1403`
`text(Mean)`  `= (1520 + 1270 + 1600 + 1310 + 1430)/6` 
`= 8418/6`  
`= $1403` 
Over a week, a pensioner drove the following distances, in kilometres, in her car.
12, 18, 11, 9, 13, 16, 12
What is his mean distance travelled in the car each day over the week?
`text(13 km)`
`text(Mean)`  `= (12 + 18 + 11 + 9 + 13 + 16 + 12)/7` 
`= 91/7`  
`= 13\ text(kilometres)` 
A spinning wheel is divided into 56 equal sectors that are coloured either red or blue.
Chablis spins the wheel and has a 1 in 8 chance of landing in a sector coloured red.
How many blue sectors are there on the spinning wheel?
`49`
`text(Number of red sectors)`  `= 1/8 xx 56` 
`= 7` 
`text(Number of blue sectors)`  `=\ text(Total sectors – Red sectors)` 
`= 56  7`  
`= 49` 
Harley has bag that contains 32 balls that are coloured either black or white.
Harley chose a ball without looking and had the chance of 3 in 8 of choosing a white ball.
How many black balls are in Harley's bag?
`20`
`text(Number of white balls)`  `= 3/8 xx 32` 
`= 12` 
`text(Number of black balls)`  `=\ text(Total balls – white balls)` 
`= 32  12`  
`= 20` 
A Cartesian plane is shown below.
Which statement is true?

`R` is located where `x < 0` and `y > 0` 

`N` is located where `x < 0` and `y < 0` 

`M` is located where `x > 0` and `y < 0` 

`Q` is located where `x < 0` and `y < 0` 
`N\ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0`
`text(Points left of the)\ y text(axis): \ x<0`
`text(Points below the)\ x text(axis): \ y<0`
`:. N\ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0\ \ text(is correct.)`
A Cartesian plane is shown below..
Which statement is true?

`S` is located where `x < 0` and `y < 0` 

`T` is located where `x < 0` and `y > 0` 

`Z` is located where `x > 0` and `y < 0` 

`Y` is located where `x = 0` and `y > 0` 
`Z\ text(is located where)\ \ x > 0\ \ text(and)\ \ y < 0`
`text(Points right of the)\ y text(axis): \ x>0`
`text(Points below the)\ x text(axis): \ y<0`
` :. Z\ text(is located where)\ \ x > 0\ \ text(and)\ \ y < 0\ \ text(is correct.)`
Alejandro makes sangria for his Spanish restaurant.
A glass of sangria has a mass of 240 grams and contains 120 millilitres of sangria.
What is the total mass of glasses that contain 3.6 litres of sangria?
kilograms
`text(7.2 kilograms)`
`text(1 litre = 1000 mL)`
`text(3.6 litres = 3600 mL)`
`text(Number of glasses)`  `= (3600)/120` 
`= 30` 
`text(S)text(ince every glass weighs 240 grams and)`
`text(1 kilogram = 1000 grams)`
`text(Total mass)`  `= 30 xx 240` 
`= 7200\ text(grams)`  
`= 7.2\ text(kg)` 
Fillon produces fresh milk.
A bottle of milk contains 500 millilitres and has a mass of 600 grams.
How many litres of milk has Fillon produced if the bottles have a total mass of 15 kilograms?
litres
`text(12.5 Litres)`
`text(1 kilogram = 1000 grams)`
`text(15 kilograms = 15 000 grams)`
`text(Number of bottles)`  `= (15\ 000)/600` 
`= 25` 
`text(S)text(ince there is 500 mL in each bottle and)`
`text(1 Litre = 1000 mL,)`
`text(Volume)`  `= 25 xx 500` 
`= 12\ 500\ text(mL)`  
`= 12.5\ text(Litres)` 
A scale diagram is shown below and represents the distances between 3 cities.
The distance from City A to City B is 84 kilometres.
What is the distance from City B to City C?
kilometres
`text(36 km)`
`text(Distance of one grid width)`  `= 84/7` 
`= 12\ text(km)` 
`text(City B and City C are 3 grids apart)`
`text(Distance City B to City C)`  `= 12 xx 3` 
`= 36\ text(km)` 
The ports A, B, and C are marked in the scale diagram below.
The distance from Port A to Port B is 35 kilometres.
What is the distance from Port B to Port C?
kilometres
`text(52.5 km)`
`text(Distance of one grid)`  `= 35/4` 
`= 8.75\ text(km)` 
`text(Port B and Port C are 6 grid widths apart)`
`text(Distance Port B to Port C)`  `= 8.75 xx 6` 
`= 52.5\ text(km)` 
Mario sketches an irregular plot of land, pictured below.
What is the perimeter of this polygon in metres?

167 m 

192 m 

244 m 

248 m 

261 m 
`248\ text{m}`
`text{Adding sides clockwise from bottom left:}`
`text{Perimeter of the shape}`  `= 50 + 15 + 30 + 17 + 14 + 13 + 34 + 45` 
`= 248 \ text{metres}` 
Jason draws an irregular shape as shown below.
What is the perimeter of this shape in metres?

113 m 

131 m 

134 m 

136m 

143 m 
`134\ text{m}`
`text{Perimeter of the shape}`  `= 8+10+3+18+19+12+24+40 ` 
`= 134 \ text{metres}` 
In a bulk food supermarket, a kilogram of pepper costs $14.
Nancy bought 2.65 kilograms of pepper for her restaurant.
How much did Nancy pay for the pepper?
$ 
`$37.10`
`text(C)text(ost of 1 kg = $14)`
`text(C)text(ost of 2 kg) = 2 xx 14 = $28`
`text(C)text(ost of 0.1 kg) = 0.1 xx $14 = $1.40`
`text(C)text(ost of 0.65 kg)`  `= 6 xx 1.4 + 0.70` 
`= $9.10` 
`:.\ text(C)text(ost of 2.65 kg)`  `= 28 + 9.1` 
`= $37.10` 
A kilogram of apples cost $8.
Danica bought 6.35 kilograms of apples.
How much did Danica pay for the apples?
$ 
`$50.80`
`text(C)text(ost of 1 kg = $8)`
`text(C)text(ost of 6 kg) = 6 xx 8 = $48`
`text(C)text(ost of 0.1 kg) = 0.1 xx 8 = $0.80`
`text(C)text(ost of 0.35 kg)`  `= 3 xx 0.8 + 0.4` 
`= $2.80` 
`:.\ text(C)text(ost of 6.35 kg)`  `= 48 + 2.80` 
`= $50.80` 
Timothy sketched a plot of land with the following measurements in metres.
What is the area of the land in square metres?
square metres 
`text(487 m)²`
`text(Divide the shape into 3 parts:)`
`text(Total Area)`  `=\ text(Area 1 + Area 2 + Area 3)` 
`= (15 xx 12) + (23 xx 10) + (1/2 xx 11 xx 14)`  
`= 180 + 230 + 77`  
`= 487\ text(m)²` 
Hana sketches a shape with the following measurements in centimetres.
What is the area of the shape sketched by Hana?
square centimetres 
`text(90 cm)²`
`text(Divide the shape into two parts.)`
`text(Total Area)`  `=\ text(Area of triangle + Area of rectangle)` 
`= (1/2 xx 4 xx 9) + (8 xx 9)`  
`= 18 + 72`  
`= 90\ text(cm)²` 
Justin went to a lolly shop to buy some sweets and spent $12.
He bought a chocolate bar that cost $5 and 7 pieces of liquorice that cost 40 cents each.
The rest of his money was spent on musk sticks that costs $0.30 each.
How many musk sticks did he buy?
`18`
`text(Money left)`  `= 12  5  (7 xx 0.40)` 
`= 72.80`  
`=$4.20` 
`:.\ text(Musk sticks)`  `= 4.2 : 0.3` 
`=4.2 : 3/10`  
`=4.2 xx 10/3`  
`= 18` 
Joanna went to the supermarket and spent $52.
She bought $15 worth of meat, 10 energy drinks costing $1.90 each and some bottles of water that cost $1.20 each.
How many bottles of water did she buy?
`15`
`text(Money left for water)`  `= 52  15  (10 xx 1.9)` 
`= 521519`  
`=$18` 
`:.\ text(Bottles of water)`  `= 18 ÷ 1.2` 
`=18 : 6/5`  
`=18 xx 5/6`  
`= 15` 
Emily walks for 17 minutes to get from her house to Diamond Station.
She then travels by train to Ruby Station.
Emily then walks 21 minutes to the supermarket where she works.
If Emily's shift starts at 6:30, what is the latest time she can leave home to arrive on time?

4:53 

5:08 

5:23 

5:38 
`5:38`
`text(Working backwards from arriving at the supermarket at 6:30)`
`text(6:30 less 21 minutes walking = 6:09)`
`text(1st train to arrive before 6:09 leaves Diamond Station at 5:55)`
`text(5:55 less than 17 minutes walking = 5:38)`
`:.\ text(Emily must leave her house by 5:38.)`
It takes Terry 32 minutes to walk from his home to Train Station A.
He then travels by train to Station C.
Terry then walks to an amusement park which takes him 18 minutes.
What is the latest time that Terry can leave his home to arrive at the amusement park by 5:00?

2:28 

2:48 

3:08 

3:28 
`3:08`
`text(Working backwards from arriving at the amusement park at 5:00)`
`text(5:00 less 18 minutes walking = 4:42)`
`text(1st train to arrive before 4:42 leaves Station A at 3:40)`
`text(3:40 less than 32 minutes walking = 3:08)`
`:.\ text(Terry must leave his house by 3:08.)`
A truck driver plans to drive from Cairns to the Gold Coast.
The driving time for the journey is 19 hours.
The driver must stop for at least 8 hours rest after every 10 hours of driving.
What is the latest time that the driver can depart Cairns on Monday to arrive in the Gold Coast at 2 pm on Tuesday?
1 am  11 am  1 pm  7 pm 




`text(11 am)`
`text(Total travel time)`  `= 19 + 8` 
`= 27\ text(hours)` 
`:.\ text(Driver must leave Cairns)`
`= 2\ text(pm Tuesday less 27 hours)`
`= 11\ text(am Monday)`
A florist uses the formula below to estimate the delivery time for an order.
`t = 11 + 3d`
where `t` is the time in minutes and `d` is the delivery distance in kilometres.
Select all the statements which are true.

A 5kilometre delivery should take 46 minutes. 

A 4kilometre delivery will take 3 minutes longer than a 3kilometre delivery. 

Every extra kilometre triples the total delivery time. 

All deliveries take at least 11 minutes. 
`text(2nd and 4th statements)`
`text(Correct statements:)`
`text(A 4kilometre delivery will take 3 minutes longer than a 3kilometre delivery.)`
`text(All deliveries take at least 11 minutes.)`
An ancient coin is made up of gold and silver in the ratio 1:3.
The coin weighs 21.65 grams.
How many grams of silver are in the ancient coin?
`5.4125`  `7.217`  `14.433`  `16.2375` 




`16.2375`
`text(Ratio)\ 1:3 > 4\ text(parts)`
`text(1 part)`  `= 21.65/4` 
`= 5.4125` 
`text(Silver weight)`  `= 3 xx 5.4125` 
`= 16.2375` 
A rectangular garden bed is 7 metres long by 4 metres wide.
The garden bed is filled with soil to a height of 50 centimetres.
How many cubic metres of soil are needed to fill the garden bed?
11  14  22  1400 




`14\ text(m³)`
`50\ text(cm) \ => \ 0.5\ text(metre)`
`text(Soil needed)`  `= 7 xx 4 xx 0.5` 
`= 14\ text(m³)` 
Sabre is saving to buy a new skateboard.
After one week she has saved $11.
She then saves the same amount of money each week.
How much money will Sabre have saved by the end of week 10?
$ 

`$74`
`text(Total saved each week (after week 1))`
`= $7`
`text(Total saved at end of week 5 = $39)`
`:.\ text(Total savings at end of week 10)`
`= 39 + (5 xx 7)`
`= 39 + 35`
`= $74`
A solar panel grid on a school roof produces an average of 8.6 kWh of energy per day.
How much energy will the grid produce for the school on average over 7 days?

kWh 
`60.2`
`text(One multiplication strategy:)`
`7xx8=56`
`7 xx 0.6 = 4.2`
`7 xx 8.6 = 56+4.2=60.2`
`:.\ text(It produces 60.2 kWh over 7 days.)`
Ken puts two cardboard squares together, as shown in the diagram below.
The squares have areas of 4 cm² and 25cm².
Ken draws a line from the bottom left to top right, and shades the region above the line.
What is the area of the shaded region?
13.5 cm²  14.5 cm²  17.5 cm²  19 cm² 




`text(17.5 cm²)`
`text(Small square → 2 cm sides)`
`text(Large square → 5 cm sides)`
`:.\ text(Shaded Area)`  `= 1/2 xx b xx h` 
`= 1/2 xx 5 xx 7`  
`= 17.5\ text(cm²)` 
Pat, Mitch and Josh entered a long distance relay as a team.
They divided the total distance into 20 equal sections.
Pat ran `9/20` of the total distance.
Mitch ran `3/20` more of the total distance than Josh.
What fraction of the total distance did Josh ran?
`4/20`  `7/20`  `8/20`  `17/20` 




`4/20`
`text(Total distance Mitch and Josh run) = 11/20`
`=>\ text(Mitch runs) = 7/20`
`=>\ text(Josh runs) = 4/20`
Students at a high school were surveyed to find whether they did exercise before school.
The graph below shows the results.
There were 150 17yearold students at the high school.
How many 17yearold students responded 'Every Day'?
`14`  `30`  `38`  `45`  `60` 





`45`
`text(30% of 17yearold responded ‘Every Day’.)`
`:.\ text(Number)`  `= 0.3 xx 150` 
`= 45` 
Genghis and Kublai are shooting arrows at a target.
Genghis shoots an arrow every 3 seconds.
Kublai shoots an arrow every 8 seconds.
They shoot their first arrow together at 10:00 am.
How many more times will they shoot arrows at exactly the same time in the next 3 minutes?
`7`
`text(Every 24 seconds, arrows shot at the same time.)`
`=>\ text(Arrows are shot at the same time:)`
`24, 48, 72, 96, 120, 144, 168\ text(seconds)`
`:. 7\ text{more times (time ≤ 180 seconds)}`
Genghis and Kublai are shooting arrows at a target.
Genghis shoots an arrow every 3 seconds.
Kublai shoots an arrow every 8 seconds.
They shoot their first arrow together at 10:00 am.
How many more times will they shoot arrows at exactly the same time in the next 3 minutes?
`7`
`text(Every 24 seconds, arrows shot at the same time.)`
`=>\ text(Arrows are shot at the same time:)`
`24, 48, 72, 96, 120, 144, 168\ text(seconds)`
`:. 7\ text{more times (time ≤ 180 seconds)}`
Rachel has a bag that contains 6 blue and 4 green balls.
She selects one ball at random and records its colour. The ball is then put back into the bag.
Rachel does this 50 times.
How many times should Rachel expect to select a green ball from the bag?
`20`
`P(text(picking green)) = 4/10 = 2/5`
`:.\ text(Expected green balls)`  `= 2/5 xx 50` 
`= 20` 
Ronald places 5 identical hexagonal tiles sidebyside to make the pattern pictured below.
Each tile has a perimeter of 24 cm and is in the shape of a regular hexagon.
What is the perimeter of the large shape, in centimetres?
cm 
`64\ text(cm)`
`text(Length of 1 side)`  `= 24 ÷ 6` 
`= 4\ text(cm)` 
`:.\ text(Perimeter)`  `= 16 xx 4` 
`= 64\ text(cm)` 
Petrol costs 158.5 cents per litre.
How much does 12 litres of petrol cost?
$ 
`$19.02`
`text(1 litre costs $1.585)`
`:.\ text(12 litres cost)`  `= 12 xx 1.585` 
`= 19.02` 
Dom times how long it takes her to get home on the bus each day.
Last year, Dom's quickest bus ride home from school was 14 minutes and 23 seconds.
She recorded the time like this.
This year, Dom's quickest bus ride home was 3 minutes and 35 seconds faster.
What is the quickest time this year?
`10:48`
`text(One strategy:)`
`text(14:23 less 3:35)`  `=\ text(11:23 less 0:35)` 
`=\ text(11:00 less 0:12)`  
`=\ text(10:48)` 
Bert and Ernie are standing in a line, waiting to go into their classroom.
There are:
In total, how many people are in the line?
`25`
`text(The lineup will be:)`
`text(10 people → Bert → 9 people → Ernie → 4 people)`
`:.\ text(Total people in line)`
`= 10 + 1 + 9 + 1 + 4`
`= 25`
During the week, a cake shop sells cupcakes for $56.00 a dozen.
On Saturday afternoon, the cost of the cupcakes is discounted by 25%.
How much will a dozen cupcakes cost on Saturday afternoon?
$ 
`$42`
`text(Price reduced by 25%) = 1/4`
`text(After the discount,)`
`text(Price)`  `= 3/4 xx 56` 
`= 3 xx 14`  
`= $42` 
Clarice has read 40 pages of a 60page book.
Select all numbers that show the fraction of the book Clarice has left to read.
`4/10`  `1/4`  `1/3` 



`2/3`  `6/4`  `2/6` 



`1/3, 2/6`
`text(Fraction left)`  `= text(pages left)/text(total pages)` 
`= 20/60` 
`:. 1/3, 2/6`
Duke looked at the calendar on 20 March.
He plans to go to a rodeo on 13 April and circled this on the calendar below.
What day of the week is 20 March?
Tuesday  Wednesday  Thursday  Saturday  Sunday 





`text(Thursday)`
`text(Working backwards:)`
`text(13 April → Sunday)`
`text(6 April → Sunday)`
`text(30 March → Sunday)`
`text(23 March → Sunday)`
`:. 20\ text(March is a Thursday)`
Ruby thinks of a number that follows the rules below.
Select all of the possible numbers that Ruby could be thinking of.
`4411`  `5115`  `5025`  `4503`  `4170`  `4602` 






`text(5025 and 4503)`
`text(5025 and 4503 satisfy all the rules.)`
Mike has 84 brochures to give out at a conference.
He puts an equal number of brochures onto each table at the conference and has none left over.
Select all of the options that could show the number of tables at the conference.
`6`  `7`  `13`  `16`  `24` 





`6 and 7`
`text(Only when 84 is divided by either 6 or 7)`
`text(will the answer be a whole number.)`
In a racing car season, the top three finishers in each race are awarded points.
Vangio was awarded a total of 25 points.
What is the greatest number of races in which Vangio could have been in the top three?
5  6  7  8 




`6`
`text(The greatest number of top 3 finishes occur with)`
`text(the following points results:)`
`8 + 5 + 3 + 3 + 3 + 3 = 25`
`:. 6\ text(events is the highest.)`
In Patrick's school, `3/7` of the students live within 5 kilometres .
There are 742 students at Patrick's school.
How many students live within 5 kilometres?
`318`
`text(Students who live within 5 km)`
`= 3/7 xx 742`
`= 3 xx 742/7`
`= 3 xx 106`
`= 318`
Ruby thinks of a number that follows the rules below.
Select all of the possible numbers that Ruby could be thinking of.
`4411`  `5115`  `5025`  `4503`  `4170`  `4602` 






`text(5025 and 4503)`
`text(5025 and 4503 are the only options that satisfy all the rules.)`
Two fishing boats record the number of tuna they catch on four fishing trips.
How many more tuna did Boat 2 catch than Boat 1 in total over the four trips.
`60`
`text(Boat 1 tuna)`  `= 140 + 120 + 40 + 55` 
`= 355` 
`text(Boat 2 tuna)`  `= 105 + 130 + 95 + 85` 
`= 415` 
`:.\ text(Extra tuna caught by Boat 2)`
`= 415  355`
`= 60`
Aragorn is fencing a paddock on his property. The total length of fencing he requires is 8.2 kilometres.
The length of the paddock is 2.8 kilometres.
Write your answer, in kilometres to one decimal place?
kilometres 
`1.3`
`text(Express as a perimeter equation:)`
`2 xx 2.8 + 2x`  `= 8.2` 
`2x`  `= 2.6` 
`:. x`  `= 1.3\ text(km)` 
A biscuit factory produces 72 000 packets of biscuits in a year.
Production is expected to increase by 1500 packets each year.
Which of these will give the best estimate of the production of the biscuit factory in 3 years' time?

`72\ 000 + 1500 xx 3` 

`(72\ 000 + 1500) xx 3` 

`72\ 000 + 1500 + 3` 

`(72\ 000 + 3) xx 1500` 
`72\ 000 + 1500 xx 3`
`text(Estimate)`  `= 72\ 000+ 1500 + 1500 + 1500` 
`= 72\ 000 + 1500 xx 3` 
Sabre want to frame a square photograph that has an area of 64 square centimetres.
Sabre makes the frame using 4 strips of aluminium.
Each strip is 4 centimetres longer than the width of the photograph.
What is the total length of the 4 strips aluminium he uses to make the frame?
`text(32 cm)`  `text(40 cm)`  `text(48 cm)`  `text(56 cm)` 




`text(48 cm)`
A brand of pasta is sold in two different packets.
What is the difference in the price per kilogram of these two packets?
$1.50  $3.00  $3.60  $7.20 




`$3.00`
`text(Convert to price per kg)`
`text(Packet 1)`
`200\ text(g) = $1.80`
`1\ text(kg) = 5 xx 1.80 = $9`
`text(Packet 2)`
`750\ text(g) = $9`
`100\ text(g) = 9.00 ÷ 7.5 = $1.20`
`1\ text(kg) = 1.20 xx 10 = $12`
`:.\ text(Difference per kg)`
`= 12  9`
`= $3.00`
55 students at a school need to choose a language to study between Japanese, Mandarin and French.
How many students chose to study Japanese?
9  11  13  28 




`28`
`text(Strategy 1)`
`text(By trial and error):`
`text(Consider option 4)`
`text(If J) = 28,\ text(M) = 18,\ text(F) = 9`
`=>\ text(total students = 55)`
`:. 28\ text(chose Japanese)`
`text{Strategy 2 (Algebra)}:`
`text(Expressing the information as equations:)`
`text(J) = text(M) + 10 …\ text{(1)}`
`text(F) = 1/2\ text(M) …\ text{(2)}`
`text(J + M + F) = 55 …\ text{(3)}`
`text{Substitute (1) and (2) into (3)}`
`text(M) + 10 + text(M) + 1/2 text(M)`  `= 55` 
`5/2 text(M)`  `= 45` 
`text(M)`  `= 18` 
`:.\ text(J)`  `= 28` 
A biscuit factory produces 72 000 packets of biscuits in a year.
Production is expected to increase by 1500 packets each year.
Which of these will give the best estimate of the production of the biscuit factory in 3 years' time?

`72\ 000 + 1500 xx 3` 

`(72\ 000 + 1500) xx 3` 

`72\ 000 + 1500 + 3` 

`(72\ 000 + 3) xx 1500` 
`72\ 000 + 1500 xx 3`
`text(Estimate)`  `= 72\ 000+ 1500 + 1500 + 1500` 
`= 72\ 000 + 1500 xx 3` 
What is the equation for the line shown?
`y = 3/2 x + 2`  `y = 3/2 x + 2`  `y = 2/3 x + 2`  `y = 2/3 x + 2` 




`y = 3/2 x + 2`
`text(Solution 1)`
`text(Graph cuts)\ y text(axis at 2)`
`text(Gradient) = text(rise)/text(run) = 3/2`
`:. y = 3/2 x + 2`
`text(Solution 2)`
`text(Graph passes through)\ (2, 5) and (2, 1)`
`text(By trial and error:)`
`text(Input each point into option 2's equation,)`
`5 = 3/2 xx 2 + 2 = 5` ✔
`1 = 3/2 xx  2 + 2 = 1` ✔
`:. y = 3/2 x + 2\ \ text(is the equation of the line.)``
Wendy went to the supermarket to buy milk, soup, pineapple and cereal.
The pineapple cost half as much as the cereal.
The cost of different combinations of her items is shown below.
What is the cost of the milk?
$1  $1.50  $2  $2.50 




`$2`
`text(S)text(ince pineapple)\ (p) = 1/2\ text(cereal)\ (c)`
`c`  `= 2p` 
`2p+p`  `= 7.50` 
`p`  `= $2.50` 
`m + s + p + c`  `= 13` 
`m + 6 + 5`  `= 13` 
`m`  `= $2` 
`:.\ text(Milk costs)\ $2`
The total entry price to a carnival for Carmel and 5 of her friends is $112.50.
What would be the cost of entry for two people?
$ 
`$37.50`
`text(C) text(ost for 1 person)`  `= 112.50/6` 
`= $18.75` 
`:.\ text(C) text(ost for 2 people)`  `= 2 xx 18.75` 
`= $37.50` 
Melinda and Cathy run the 100 metre sprint in their school athletics carnival.
A device tracks their progress and the results are graphed below.
Melinda starts quickly and passes the 75 metre mark after 10 seconds, slowing down as the race progresses.
Cathy is slower but runs the whole race at the same speed.
How long after Melinda did Cathy pass the 75 metre mark in the race?
seconds 
`5`
`text(Melinda passes 75 metre mark at 10 seconds.)`
`text(Cathy passes at 15 seconds.)`
`:.\ text(Cathy passes 5 seconds after Melinda.)`
This drawing shows how a large rectangular prism is cut into 3 objects.
Step 1: A medium rectangular prism is cut from a large rectangular prism.
Step 2: The smaller rectangular prism is cut into 2 identical triangular prisms.
What is the total number of faces of the three pieces after Step 2, including the bases?
faces 
`19`
`text(Faces on triangular prism = 5)`
`text{Faces on larger rectangle (after step 1) = 9}`
`:.\ text(Total faces of 3 shapes)`
`= (2 xx 5) + 9`
`= 19`
This picture shows the length of three shot put throws at a school athletics carnival.
Shot put 2 lands exactly halfway between shot put 1 and shot put 3.
What is the distance between the throw line and shot put 2?
`6.0\ text(metres)`
`text(Difference between shot put 1 and 3)`
`= 6.9  5.1`
`= 1.8\ text(m)`
`:.\ text(Distance from throw line to shot put 2)`
`= 5.1 + 0.5 xx 1.8`
`= 6.0\ text(metres)`