Ratios & FDP (Edexcel IGCSE Maths B): Revision Note

In these types of questions it is really important to read the question carefully, so that you are clear about which bits are referring to which quantity.

Give your final answer in the form asked for by the question (fraction, ratio, or percentage).

A shop sells only two flavours of crisps - Stilton Surprise and Pickled Haggis.  Packages of those two flavours of crisps only occur in two sizes - regular and jumbo.

The ratio of packages of Stilton Surprise crisps to packages of Pickled Haggis crisps in the shop is 7:3.

30% of the packages of Stilton Surprise crisps are regular sized.
$\frac{2}{5}$ of the packages of Pickled Haggis crisps are regular sized.

What percentage of all the packages of crisps in the shop are jumbo sized?

Answer:

Method 1

First find the fractions of each type of crisp
The ratio divides the crisps into 7+3=10 parts
7 of those parts are Stilton Surprise, and 3 of them are Pickled Haggis

$$\begin{gathered} \frac{7}{7+3}=\frac{7}{10}\mathrm{are}\mathrm{Stilton}\mathrm{Surprise} \\ \frac{3}{7+3}=\frac{3}{10}\mathrm{are}\mathrm{Pickled}\mathrm{Haggis} \end{gathered}$$

30% of the Stilton Surprise are regular sized
So multiply 7/10 by 0.3 to find the percentage that are Stilton Surprise and regular sized

$$\begin{gathered} \frac{7}{10}\times 0.3=\frac{7}{10}\times \frac{3}{10}=\frac{21}{100} \\ \frac{21}{100}=0.21 \\ \mathrm{So}21\%\mathrm{are}\mathrm{regular}\mathrm{sized}\mathrm{Stilton}\mathrm{Surprise} \end{gathered}$$

2/5 of the Pickled Haggis are regular sized
So multiply 3/10 by 2/5 to find the percentage that are Pickled Haggis and regular sized

$$\begin{gathered} \frac{3}{10}\times \frac{2}{5}=\frac{6}{50} \\ \frac{6}{50}=\frac{12}{100}=0.12 \\ \mathrm{So}12\%\mathrm{are}\mathrm{regular}\mathrm{sized}\mathrm{Pickled}\mathrm{Haggis} \end{gathered}$$

Add those together to find the percentage that are regular sized

$21+12=33\%\mathrm{regular}\mathrm{sized}$

And finally subtract 33% from 100% to find the percentage that are jumbo sized

$100-33=67$

67% are jumbo sized

Method 2

Start by assuming (for example) that there are 100 packages of crisps in the shop
The ratio divides the crisps into 7+3=10 parts
So divide 100 by 10 to find how many packages are in 1 part

$100÷10=10\mathrm{packages}$

7 of those parts are Stilton Surprise, and 3 of them are Pickled Haggis
So multiply 10 by 7 and by 3 to find out how many packages of each type there are

$$\begin{gathered} 7\times 10=70\mathrm{are}\mathrm{Stilton}\mathrm{Surprise} \\ 3\times 10=30\mathrm{are}\mathrm{Pickled}\mathrm{Haggis} \end{gathered}$$

30% of the Stilton Surprise are regular sized
So multiply 70 by 0.3 to find how many are Stilton Surprise and regular sized

$\begin{array}{rcl}70\times 0.3& =& 70\times \frac{3}{10}\\ & =& \frac{210}{10}\\ & & \\ & =& 21\mathrm{are}\mathrm{regular}\mathrm{sized}\mathrm{Stilton}\mathrm{Surprise}\end{array}$

2/5 of the Pickled Haggis are regular sized
So multiply 30 by 2/5 to find how many are Pickled Haggis and regular sized

$\begin{array}{rcl}30\times \frac{2}{5}& =& \frac{60}{5}\\ & & \\ & =& 12\mathrm{are}\mathrm{regular}\mathrm{sized}\mathrm{Pickled}\mathrm{Haggis}\end{array}$

Add those together to find how many in total are regular sized

$21+12=33\mathrm{are}\mathrm{regular}\mathrm{sized}$

Subtract 33 from 100 to find how many are jumbo sized

$100-33=67\mathrm{are}\mathrm{jumbo}\mathrm{sized}$

And finally turn that into a percentage out of 100

$\frac{67}{100}=0.67$

67% are jumbo sized