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Algebra, NAP-K3-NC03

A soccer club receives 9 boxes containing 35 club jerseys each.

It then gives 15 jerseys to every team in the club and there are no jerseys left over.

How many teams are in the club?

`18` `21` `26` `50`
 
 
 
 
Show Answers Only

`21`

Show Worked Solution

`text(Let)\ n =\ text(number of teams)`

`15 xx n` `= 9 xx 35`
`3 xx 5 xx n` `= 3 xx 3 xx 7 xx 5`
`:. n` `= 3 xx 7`
  `= 21`

Algebra, NAP-K3-CA27

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
 
 
 
 
Show Answers Only

`$2`

Show Worked Solution

`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`

Algebra, NAP-K3-CA23

Leia does a writing course that charges a fee per session and a one off $80 administration fee.

The overall cost (`C`) is represented by the formula  `C = 25s + 80`  where `s` is the number of sessions Leia attends.

Leia attends 6 sessions in total.

How much does she pay?

`$80` `$91` `$230` `$630`
 
 
 
 
Show Answers Only

`$230`

Show Worked Solution
`text(C)text(ost)` `= 25s + 80`
  `= 25 xx 6 + 80`
  `= $230`

Algebra, NAP-D3-CA12

Billy is setting up tables for a comedy night at his club.

An  X  is placed for every available seat at a table, as shown below.
 

  
Which of these rules can be used to work out how many people can sit on any row of tables?

 
 `text(number of tables) xx 6`
 
 `text(number of tables) ÷ 2 - 2`
 
 `text(number of tables) xx 4 + 2`
 
 `text(number of tables) xx 4 - 2`
Show Answers Only

`text(number of tables) xx 4 + 2`

Show Worked Solution

`text(Consider Option 3:)`

`text(1st table:)\ \ 1 xx 4 +2 = 6\ text(people)`

`text(2nd table:)\ \ 2 xx 4 +2 = 10\ text(people)`

`text(3rd table:)\ \ 3 xx 4 +2 = 14\ text(people)`

 

`:.\ text(number of tables) xx 4 + 2\ \ text(is the correct rule.)`

Algebra, NAP-D3-CA20

Matt is 12 years younger than Mark.

Which statement is correct?

 
 `text(Mark's age)\ +\ text(Matt's age) = 12`
 
 `text(Mark's age) = text(Matt's age) + 12`
 
 `text(Matt's age)\ -\ text(Mark's age) = 12`
 
 `text(Matt's age) = text(Mark's age) + 12`
Show Answers Only

`text(Mark’s age) = text(Matt’s age) + 12`

Show Worked Solution

`text(Mark’s age) = text(Matt’s age) + 12`

Algebra, NAP-E3-NC28 SA

Damon bought 2 identical bags of salt for his swimming pool.

After he used  `2/3`  of one bag in the pool, he had a total of 20 kilograms of salt left.

How many kilograms of salt were in one full bag?

  kilograms
Show Answers Only

`15`

Show Worked Solution

`text(Let)\ \ \ S =\ text(weight of 1 bag of salt)`

`1/3S + S` `= 20`
`4/3 S` `= 20`
`:. S` `= (3 xx 20)/4`
  `= 15\ text(kg)`

Algebra, NAP-F3-CA17

There are 74 year 7 students enrolled at a school.

There are 12 more girls enrolled than boys.

How many boys are enrolled in year 7?

`30` `31` `43` `62`
 
 
 
 
Show Answers Only

`31\ text(boys)`

Show Worked Solution

`text(Let)\ \ n = text(number of boys enrolled)`

`=> n + 12 = text(number of girls enrolled)`

`n + n + 12` `= 74`
`2n` `= 62`
`n` `= 31`

 

`:.\ text(There are 31 boys enrolled.)`

Algebra, NAP-G3-NC26 SA

Gina and Bob are dog breeders.

The total number of dogs they currently own is 21.

Gina owns 5 more dogs than Bob.

How many dogs does Gina own?
Show Answers Only

`13`

Show Worked Solution
`text(Let)\ \ n` `=\ text(number of dogs Bob owns)`
`=> n + 5` `=\ text(number of dogs Gina owns)`

 

`n + n + 5` `= 21`
`2n` `= 16`
`n` `= 8`

 
`:.\ text(Gina owns 13 dogs.)`

Algebra, NAP-G3-NC01

Mike and Georgia saved $120 together.

Georgia saved twice as much money as Mike.

How much money did Georgia save?

`$20` `$40` `$80` `$240`
 
 
 
 
Show Answers Only

`$80`

Show Worked Solution

`text(Let)\ \ x =\ text(Mike’s savings)`

`2x + x` `=120`
`3x` `=120`
`x` `=40`

 

`:.\ text(Georgia saved $80.)`

Algebra, NAP-G3-CA21

Pasta is sold in bags of 3 sizes: small, medium, and large.

A medium bag of pasta costs $3.25 more than a small bag.

A large bag of pasta costs $4.75 more than a small bag.

Which equation correctly states the cost of a medium bag of pasta?

 
 cost of a medium pasta = cost of a large pasta – $1.50
 
 cost of a medium pasta = cost of a large pasta – $3.25
 
 cost of a medium pasta = cost of a large pasta – $4.75
 
 cost of a medium pasta = cost of a large pasta – $8
Show Answers Only

`text(cost of a medium pasta = cost of a large pasta – $1.50)`

Show Worked Solution

`text(The extra cost of a large pasta over a medium pasta)`

`=$4.75 – $3.25`

`=$1.50`
 

`:.\ text(C)text(ost of a medium pasta = cost of a large pasta – $1.50)`

Algebra, NAP-G3-CA15

Kate takes part in a swimathon to raise money for charity.

Her grandmother sponsors her $20 in total.

Her uncle sponsors her $1.25 for each lap of the pool she swims.

In order to raise $100, how many laps does Kate need to swim?

`5`  `10` `64` `80` `88`
 
 
 
 
 
Show Answers Only

`64\ text(laps)`

Show Worked Solution

`text(Let)\ \ x = text(number of laps that Kate need to swim)`

`100` `= 1.25x + 20`
`1.25x` `= 100 – 20`
`:. x` `= 80/1.25`
  `= 64\ text(laps)`

Algebra, NAP-H3-NC21

Karen and Kim are sisters and share a bedroom.

They want their beds positioned the same distance from the centre of the room.
 

 

 
What is the distance `x` from the edge of each bed to the middle of the room?

`1.25\ text(m)` `2.25\ text(m)` `2.50\ text(m)` `2.75\ text(m)` `5.25\ text(m)`
 
 
 
 
 
Show Answers Only

`1.25\ text(m)`

Show Worked Solution

`text(Half the room is 4 m wide.)`

`:. x` `= 4 – (1 + 1.75)`
  `=4-2.75`
  `=1.25\ text(m)`

Algebra, NAP-H3-CA20

An unknown number is added to 6.

The result is multiplied by 3 to give an answer of 12.

Which of these is the unknown number?

`− 3` `− 2` `2` `30`
 
 
 
 
Show Answers Only

`−2`

Show Worked Solution

`text(Working backwards:)`

`text(S)text(ince 4 is multiplied by 3 to make 12,)`

`=>\ text(unknown + 6 = 4)`
 

`:.\ text(Unknown number = − 2)`

Algebra, NAP-I3-NC21

Stu and Tarly collect sea-shells on the beach.

Tarly collects 3 times as many sea-shells as Stu plus an additional 5.

Let  `s`  be the number of shells Stu collects.

Which expression correctly shows the number of shells Tarly collects?

`(3 × s) + 5` `3 + (5 × s)` `(s ÷ 3) - 5` `3 - (s ÷ 5)`
 
 
 
 
Show Answers Only

`(3 × s) + 5`

Show Worked Solution

`(3 × s) + 5`

Algebra, NAP-I3-NC15

Lee pays a monthly membership of $36 to have unlimited entry to the local swimming pool.

If she does squad training, she needs to pay an extra $8 per session to the swim coach.

If Lee does `n` squad sessions in a month, which expression represents her monthly bill?

`8n` `36n` `36n + 8` `36 + 8n`
 
 
 
 
Show Answers Only

`36 + 8n`

Show Worked Solution

`text(Monthly membership = $36)`

`text(C)text(ost of)\ n\ text(squad sessions =)\ $8n`

`:.\ text(Total monthly bill)\ = 36 + 8n`

Number, NAP-C3-NC31 SA

Billy has some bananas to give to his friends.

If he gives each friend 3 bananas. he will have 5 left over.

He cannot give each friend 4 bananas because he would need 7 more bananas.

How many bananas does Billy have?

 
Show Answers Only

`41`

Show Worked Solution

`text(Let)\ \ n=\ text(the number of Billy’s friends)`

`text(The information given tells us that:)`

`3n + 5` `=\ text(# of bananas)`
`4n-7` `=\ text(# of bananas)`
`:. 4n-7` `=3n+5`
`n` `=12`

 
`:.\ text(Number of bananas Billy has)`

`=(3 xx 12) + 5`

`=41`

Algebra, NAP-C3-CA19

Kate is 4 years older than Jess.

Sarah is 6 years older than Jess.

Which equation shows how Kate's age relates to Sarah's age?

 
 `text(Kate's age) = text(Sarah's age) + 2`
 
 `text(Kate's age) = text(Sarah's age) - 2`
 
 `text(Kate's age) = text(Sarah's age) + 10`
 
 `text(Kate's age) = text(Sarah's age) - 10`
Show Answers Only

 `text(Kate’s age) = text(Sarah’s age) – 2`

Show Worked Solution

`text(Kate is 2 years younger than Sarah,)`

`:.\ text(Kate’s age) = text(Sarah’s age) – 2`