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Number, NAP-K4-CA40 SA

Jagger makes and supplies fresh muffins to cafes in the city.

As the number of muffins he makes increases, the cost to make each muffin decreases.

He sells the muffins for the same price and takes the orders in multiples of 6.
 

 
Assuming the cost per muffin continues to follow the decreasing trend in the table, how much profit will Jagger make on an order of 30 muffins?

$  
Show Answers Only

`$132.00`

Show Worked Solution

`text(Sale price of 1 muffin)`

`= 31.50 ÷ 6`

`= $5.25`

 
`text{C} text{ost of 1 muffin (order of 30)}`

`= 1.00 – 0.15`

`= $0.85`
 

`:.\ text(Profit)` `= text(sales) – text(cost)`
  `= 30 xx 5.25 – 30 xx 0.85`
  `= $132.00`

Filed Under: Financial Maths, Financial Maths Tagged With: Band 10, smc-3174-30-Profit/Cost/Revenue, smc-892-30-Profit/Cost/Revenue

Algebra, NAP-K4-CA15

Surf Grommets charge an hourly rate for surfing lessons and add a one-off charge of $45 for insurance.

The overall cost `(C)` is represented by the formula, `C = 30h + 45`, where `h` is the number of hours of lessons.

Mark has 11 hours of lessons with Surf Grommets.

How much does he pay?

$86 $330 $375 $825
 
 
 
 
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`$375`

Show Worked Solution
`C` `= 30 xx 11 + 45`
  `= 330 + 45`
  `= $375`

Filed Under: Financial Maths, Financial Maths, Financial Maths, Harder Equations, Harder Equations Tagged With: Band 7, smc-3144-30-Profit/Cost/Revenue, smc-3174-30-Profit/Cost/Revenue, smc-892-30-Profit/Cost/Revenue

Number, NAP-K4-CA06

Onyx makes four dream catchers for a total cost of $160.

He sells two of the dream catchers for $40 each and another for $55.

For what price must he sell the fourth dream catcher to achieve a profit?

 
more than $25
 
less than $25
 
exactly $25
 
a profit is not possible
Show Answers Only

`text(more than $25)`

Show Worked Solution

`text(C) text(ost) = $120`

`text(Sales) = 2 xx 40 + 55 = $135`

`text(Profit occurs when sales price)\ >\ text(cost)`
 

`:.\ text(Sales price of 4th dream catcher must be more than $25)`

Filed Under: Financial Maths, Financial Maths Tagged With: Band 7, smc-3174-30-Profit/Cost/Revenue, smc-892-30-Profit/Cost/Revenue

Number, NAP-J4-CA06

Tran is a baker and sells 100 loaves of bread at the markets. Each loaf costs him $2.25 to make.

He sells 80 loaves for $4.95 each.

In the last hour of the market, he sells the last 20 loaves for $2 each.

What is the total profit or loss of the 100 loaves?

`−$5.00` `$211.00` `$216.00` `$436.00`
 
 
 
 
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`$211.00`

Show Worked Solution
`text(Total profit/loss)` `=\ text(sales revenue – costs)`
  `=(80 xx 4.95 + 20 xx 2) – (100 xx 2.25)`
  `= 436 – 225`
  `= $211`

Filed Under: Financial Maths, Financial Maths, Financial Maths Tagged With: Band 7, smc-3144-30-Profit/Cost/Revenue, smc-3174-30-Profit/Cost/Revenue, smc-892-30-Profit/Cost/Revenue

Number, NAP-C4-CA24

This graph shows the cost of a tow truck that charges a flat fee plus a cost per kilometre.
 

 
The expression to calculate the cost is

 
`40 + (6 xx text{kilometres towed)}`
 
`40 + (10 xx text{kilometres towed)}`
 
`40 + (16.6 xx text{kilometres towed)}`
 
`40 + (100 xx text{kilometres towed)}`
Show Answers Only

`40 + (10 xx text{kilometres towed)}`

Show Worked Solution

`text{The flat fee is $40 (i.e. the cost for 0 km).}`

`text(Each kilometre towed increases the cost of the)`

`text(tow truck by $10.)`

`40 + (10 xx text{kilometres towed)}`

Filed Under: Financial Maths, Financial Maths Tagged With: Band 9, smc-3174-30-Profit/Cost/Revenue, smc-892-30-Profit/Cost/Revenue

Number, NAP-D4-CA29 SA

Chloe sells beach umbrellas from her beach shack for $20 each.

Chloe pays $480 rent per week for her beach shack and each beach umbrella costs her $12.

How many beach umbrellas does Chloe need to sell per week to equal her weekly costs?

Show Answers Only

`60`

Show Worked Solution

`text(Selling price) = $20`

`text(C)text(ost per umbrella) = $12`

 `text(Profit per umbrella)` `= $20 – 12`
  `= $8`

 

`:.\ text(Umbrellas needed to pay for weekly costs)`

`=480 ÷ 8`

`= 60`

Filed Under: Financial Maths, Financial Maths Tagged With: Band 9, smc-3174-30-Profit/Cost/Revenue, smc-892-30-Profit/Cost/Revenue

Number, NAP-G4-NC06

12 people went to Sea World together in a bus.

Entry into Sea World was $44 per person and the total cost of the bus was $120.

Which expression shows the total cost of the trip for everybody?

`(44 + 120) xx 12` `44 + 12 + 120` `(12 xx 44) + 120` `12 xx 44`
 
 
 
 
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`(12 xx 44) + 120` 

Show Worked Solution

`text(Total cost of entry to Sea World)`

`=12 xx $44`

`text(Total cost of bus)\ = $120\ \ text{(given)}`

`:.\ text(Total cost of the trip for everybody)`

`= (12 xx 44) + 120`

Filed Under: Financial Maths, Financial Maths Tagged With: Band 7, smc-3174-30-Profit/Cost/Revenue, smc-892-30-Profit/Cost/Revenue

Measurement, NAP-H4-CA28 SA

A cement slab is laid in Bob's backyard that forms a 9 m × 3 m rectangle.
 

 
 

Bob is going to tile around the edge of his slab using one row of  300 mm × 300 mm tiles.

He will use 50% black tiles costing $8 per tile and 50% white tiles costing $5 per tile.

What is the total cost of the tiles he used?

$ 
Show Answers Only

`$546`

Show Worked Solution

`text{Tiles used on length (including end tiles)}`

`= 9/0.3 + 2`

`= 32`

 

`text(Tiles used on width) = 3/0.3 = 10`

 

`:.\ text(Total tiles used)` `= 2 xx (32 + 10)`
  `= 84`

 

`:.\ text(C) text(ost)` `= (42 xx 8) + (42 xx 5)`
  `= 336 + 210`
  `= $546`

Filed Under: Financial Maths, Financial Maths, Perimeter, Area and Volume, Perimeter, Area and Volume Tagged With: Band 10, smc-3174-30-Profit/Cost/Revenue, smc-3183-20-Area, smc-3183-70-Tiling, smc-669-20-Area, smc-669-70-Tiling, smc-892-30-Profit/Cost/Revenue

Algebra, NAP-I4-NC08

Ali joins a gym that has a fortnightly fee of $33.

Members pay an extra $12 per session if they want to do a special yoga class.

Which expression represents Ali's fortnightly gym bill if she does  `x`  yoga classes during the fortnight?

`12x` `33x` `33x + 12` `33 + 12x`
 
 
 
 
Show Answers Only

`33 + 12x`

Show Worked Solution
`text(Fortnightly cost)` `=\ text(fee + yoga classes)`
  `=\ 33 + 12x`

Filed Under: Basic Algebra, Basic Algebra, Financial Maths, Financial Maths Tagged With: Band 7, smc-3174-30-Profit/Cost/Revenue, smc-3179-50-Word problems, smc-683-50-Word problems, smc-892-30-Profit/Cost/Revenue

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