Functional Skills: Problems Involving Money

Skill 1: Converting between pounds (£) and pence (p)

Many questions require you to add and subtract values in both pounds (£) and pence (p), so you need to be able to switch between the two.

• To go from pounds to pence, multiply by 100
• To go from pence to pounds, divide by 100

 

Example: To convert £3.27 into pence, we multiply 3.27 by 100

So,

£3.27=327p

 

Example: To convert 47p into pounds, we divide 47 by 100

So,

47p =£0.47

Skill 2: Rate of Pay

The rate of pay is the cost of something per unit of time, for example a phone call may cost 25p per minute or someone may get paid £11.70 per hour.

Often questions require you to combine a rate of pay with a fixed fee, or combine two different rates of pay.

Example: Sarah earns \textcolor{red}{£9.80} per hour and works \textcolor{limegreen}{30} hours in one week. She earned \textcolor{red}{£32.50} in tips.

How much did she earn in the week?

 

First calculate how much she earns from her hourly rate of pay: \textcolor{limegreen}{30}\times \textcolor{red}{£9.80}=£294

Then calculate her total earnings for the week: £294+\textcolor{red}{£32.50}=\textcolor{black}{£326.50}

 

Example: Stephen wants to re-tile his bathroom and also replace his shower.

A tiler charges \textcolor{red}{£24} per hour and says it will take \textcolor{limegreen}{11} hours work.

A plumber charges \textcolor{red}{£28.50} per hour and says it will take \textcolor{limegreen}{9} hours to fit the work.

How much will it cost Stephen in total to do both jobs?

 

Cost of re-tiling his bathroom: \textcolor{red}{£24} \times \textcolor{limegreen}{11}=£264

Cost of replacing his shower: \textcolor{red}{£28.50} \times \textcolor{limegreen}{9}=£256.50

Total Cost: £264+£256.50=\textcolor{black}{£520.50}

Skill 3: Discounts and Increases as Percentages

Often questions ask you to find the new price of an item after it has been increased or discounted by a certain percentage.

For LEVEL 1 you will only see discounts and increases given in multiples of 5\%, where as for LEVEL 2 you will need to work with all percentages.

You may need to re-visit percentage increase and percentage decrease to help you answer these types of questions.

 

Price Decrease

If a product’s price has been reduced by a percentage, we take this value away from 100\% and then convert this value into a decimal to then multiply it by the original price.

Example: A pair of trainers costs \textcolor{orange}{£45}. If there is a sale on which gives \textcolor{blue}{20\%} off the price, what will be the new price of the trainers?

100\% - 20\%=80\%=0.8

New price of the trainers: \textcolor{orange}{£45}\times0.8=\textcolor{black}{£36}

 

Price Increase

If a product’s price has been increased by a percentage, we add this value to 100\% and then convert this value into a decimal to then multiply it by the original price.

Example: Lucy bought a house for \textcolor{orange}{£210000} last year, she has the house valued 1 year later and is told that the value of the house has increased by \textcolor{blue}{10\%}. Calculate the new value of the house.

100\%+10\%=110\%=1.1

New value of house: 1.1 \times \textcolor{orange}{£210000}=\textcolor{black}{£231000}

 

Note: Alternatively, we could have found what 10\% of £210000 was and then added this to the original value of the house.

Skill 4: Discounts as Fractions

You could also be asked to find the new price of an item after a discount in terms of a fraction has been applied.

You may need to re-visit fractions to help you answer these types of questions.

 

Example: A bike costs \textcolor{orange}{£330}. If there is a sale on which gives \textcolor{blue}{\dfrac{2}{5}} off the price, what will be the new price of the bike?

First, calculate \dfrac{2}{5} of the original price:

2 \div 5 \times \textcolor{orange}{£330} = £132

Then, subtract this from the original price of the bike:

\textcolor{orange}{£330} - £132 = \textcolor{black}{£198}

Skill 5: Percentage Profit

Percentage profit is the profit of selling an item as a percentage of the total costs involved.

\text{\textcolor{purple}{Profit}} = \text{\textcolor{blue}{Selling Price}} - \text{\textcolor{red}{Costs}}

\textcolor{limegreen}{\% \text{ Profit}}=\dfrac{\text{\textcolor{purple}{Profit}}}{\text{\textcolor{red}{Costs}}}\times100

Example: Gareth buys an old car for £1250, he then buys some replacement parts for £250. He sells the car on for £2100, calculate his percentage profit.

Profit =£2100-(£1250+£250)=£600

\% Profit =\dfrac{600}{1500}\times100=40\%