There are 32 people in a meeting room.
The ratio of females to males in the room is 9 to 7.
How many females need to leave the room so that the ratio of females to males in the room is 1 to 1?
Aussie Maths & Science Teachers: Save your time with SmarterEd
There are 32 people in a meeting room.
The ratio of females to males in the room is 9 to 7.
How many females need to leave the room so that the ratio of females to males in the room is 1 to 1?
`4\ text(females)`
`text(Females : Males) = 9 : 7`
`=> 18\ text(females and 14 males are in the room.)`
`:.\ text(If 4 females leave, the ratio)`
`text(becomes 1 : 1)`
Which expression is equivalent to `2x^2 - 8x + 4x^3?`
`2(x^2 - 4x + 4x^3)` | `2x (x - 4 + 4x^2)` | `x^2 (2 - 4 + 4x)` | `x (2x - 8 + 4x^2)` |
|
|
|
|
`x (2x-8 + 4x^2)`
`x (2x-8 + 4x^2)`
`= 2x^2-8x + 4x^3`
Kate is freezing chicken stock liquid as a treat for her dog in summer.
One container requires 0.65 litres of liquid to fill it.
How many millilitres of liquid chicken stock would Kate need to fill up one container?
millilitres |
`650\ text(millilitres)`
`text(Liquid required)` | `= 0.65 xx 1000` |
`= 650\ text(mL)` |
Over 5 games, Faf scored the following runs when playing cricket.
`7, 3, 18, 1, 62, 35`
What was his mean score?
`21`
`text(Mean)` | `= (7 + 3 + 18 + 1 + 62 + 35) ÷ 6` |
`= 126 ÷ 6` | |
`= 21` |
Chakra earns $23.88 per hour at a homewares shop.
In one week, she worked `15 1/4` hours.
She used the money to buy incense scented candles for her friends.
Each candle costs $31.25.
What is the maximum number of candles Chakra can buy?
candles |
`11`
`text(Money earned)` | `= 15 1/4 xx 23.88` |
`= $364.17` |
`:.\ text(Maximum candles)` | `= 364.17/31.25` |
`= 11.65…` | |
`= 11\ text{candles (must round down)}` |
Complete the following equation,
`4^4 - 3^3 + 2^2 - 1^1 = ` |
`232`
`4^4 – 3^3 + 2^2 – 1^1`
`= (4 xx 4 xx 4 xx 4) – (3 xx 3 xx 3) + (2 xx 2) – 1`
`= 256 – 27 + 4 – 1`
`= 232`
An African wildlife reserve has 480 elephants.
Of the 480 elephants, `5/8` of them weigh more than 4000 kilograms.
Of the elephants that weigh more than 4000 kilograms, `1/4` weigh more than 6000 kilograms.
How many elephants in the reserve weigh more than 6000 kilograms?
`75`
`text(Number of elephants > 4000 kg)`
`= 5/8 xx 480`
`= 300`
`text(Number of elephants > 6000 kg)`
`= 1/4 xx 300`
`= 75`
Manou's French restaurant took in $8321.70 on Valentine's Day.
Pete's Paleo restaurant took in $3190.85 on the same night.
How much more money did Manou's restaurant take in than Pete's on Valentine's Day?
$ |
`$5130.85`
`$8321.70 – $3190.85`
`= $5130.85`
Harmony is buying eggs for her vegetarian restaurant.
Each carton contains 12 eggs.
If she needs 86 eggs, how many cartons will she need to buy?
`text(8 cartons)`
`86 ÷ 12 = 7\ text(remainder 2)`
`:.\ text(Harmony need 8 cartons.)`
Sierra creates a muesli which is a mixture of 4 different types of fruit and nuts.
She makes 400 grams of the mixture and weighs each ingredient as follows:
How many grams of apricots are in the 400 grams of muesli?
`96\ text(grams)`
`text(Mass of macadamias)` | `= 40 text(%) xx 400` |
`= 160\ text(grams)` |
`text(Weight of remaining ingredients)`
`= 400-160`
`= 240\ text(grams)`
`text(Let)\ \ x = text(weight of apricots)`
`x + x + 1/2x` | `= 240` |
`:. x` | `= 240/2.5` |
`= 96\ text(grams)` |
A rectangular prism is made by stacking 6 identical triangular prisms, as pictured below.
What is the volume of one triangular prism, in cubic centimetres?
cubic centimetres |
`27\ 552 text(cm³)`
`text(Volume of rectangular prism)`
`= 42 xx 48 xx 82`
`= 165\ 312\ text(cm³)`
`:.\ text(Volume of 1 triangular prism)`
`= 165\ 312 ÷ 6`
`= 27\ 552\ text(cm³)`
Sequoia owns a farm with a rectangular paddock.
She increases the area of the paddock by adding land that changes it into the shape of a trapezium.
What is the area of Sequoia's new paddock, in square metres?
square metres |
`2599\ text(m²)`
`A` | `= 1/2h(a + b)` |
`= 1/2 xx 46 xx (42 + 71)` | |
`= 2599\ text(m²)` |
In this inequality `n` is a whole number.
`5/n < 3/5`
What is the smallest possible value for `n` to make this inequality true?
`9`
`5/n` | `< 3/5` |
`3n` | `> 25` |
`n` | `> 25/3` |
`n` | `> 8.33…` |
`:.\ text(Smallest)\ n = 9`
The sale price of a second hand car is $4800.
Zilda buys the car for 25% off the sale price.
Zilda has a discount voucher that gives her a further $240 off the sale price.
What percentage of the original price does Zilda pay for the car?
% |
`text(70%)`
`text(Sale price)` | `= $4800-(25% xx 4800)` |
`= 75% xx 4800` | |
`= $3600` |
`text(Purchase price)` | `= 3600-240` |
`= $3360` |
`:.\ text(Percentage of original price)`
`= 3360/4800 xx 100`
`= 70 text(%)`
Huckleberry opens a savings account and deposits $1200 into it.
He makes no more deposits and earns simple interest on his original deposit at 2.5% each year.
How much interest will Huckleberry earn after 3 years?
$ |
`$90`
`text(Interest earned)` | `= Prn` |
`= 1200 xx 2.5/100 xx 3` | |
`= $90` |
Skye sells 18 mini-cakes of soap at the farmers market for a total of $9.90.
Dharma sells 30 cakes of soap at the same price per cake of soap as Skye.
In total, how much more does Dharma make than Skye?
$ |
`$6.60`
`text(C)text(ost of 1 soap)` | `= 9.90 ÷ 18` |
`= $0.55` |
`text(C)text(ost of 30 soaps)` | `= 30 xx 0.55` |
`= $16.50` |
`:.\ text(Extra sales)` | `= 16.50-9.90` |
`= $6.60` |
Indigo is a lawyer.
She charges $250 to look at a case and then a fixed price for each minute she spends on the case.
The graph below shows Indigo's charge based on the number of minutes she spends on the case.
How much will Indigo charge for a case that takes 60 minutes of her time?
$ |
`$430`
`text(Initial charge = $250)`
`text(From the graph,)`
`=>\ text(50 minute matter costs $400)`
`:.\ text(C)text(ost per minute)` | `= (400-250)/50 = $3` |
`:.\ text(C)text(ost of 60 minute matter)`
`= 250 + 60 xx 3`
`= $430`
A candle maker increases the price of a candle from $20 to $25.
What is the percentage increase in his price?
% |
`text(25%)`
`text(Price increase) = 25 – 20 = $5`
`text(Percentage increase)` | `= 5/20 xx 100` |
`= 0.25 xx 100` | |
`= 25text(%)` |
Fifty football fans were surveyed about modes of transport they took to get to the game.
The diagram is missing some information.
How many caught both a train and a bus to get to the game?
`13`
`text(Interpreting the Venn diagram:)`
`text(S)text(ince fifty fans surveyed,)`
`:.\ text(Number that took both train and bus)`
`= 50 – (20 + 9 + 8)`
`= 13`
A Nimbin high school has 1000 students enrolled.
27 of the 1000 students have the first name Dusk.
Write this as a decimal.
`0.027`
`27 ÷ 1000 = 0.027`
Abigail has a 0.65 metre length of rope.
She cuts a 350 millimetre piece off it.
How long is the remaining length of rope?
millimetres |
`300\ text(mm)`
`text(Length remaining)` | `= (0.65 xx 1000) – 350` |
`= 650 – 350` | |
`= 300\ text(mm)` |
Mickey cuts a quarter circle out of a full circle, as shown below.
If the circle's radius is 7 cm, what is the perimeter of the shape, to the nearest centimetre?
cm |
`47\ text{(nearest cm)}`
`text(Perimeter)` | `=\ text(arc + 2 × radii)` |
`= (3/4 xx 2 xx pi xx r) + 2 r` | |
`= 3/4 xx 2 xx pi xx 7 + 2 xx 7` | |
`= 46.986…` | |
`= 47\ text{cm (nearest cm)}` |
Ziggy throws darts at a board split into 4 sections and records which section they hit.
Based on Ziggy's data, what is the probability that a dart he throws will land in section 1 or 2?
Express your answer as a percentage rounded to the nearest tenth.
% |
`text{75.3% (nearest tenth)}`
`text(Number of throws)` | `= 45 + 22 + 13 + 9` |
`= 89` |
`:.\ text{Probability (1 or 4)}` | `= {(45 + 22)}/89` |
`= 67/89` | |
`= 0.7528…` | |
`= 75.3 text{% (nearest tenth)}` |