Solving best buy problems

In a nutshell

Best value problems are a very useful real world application of ratios. They can help get the best value for money.

Solving best value problems

To solve best value problems, use ratios to find how much is in one penny (or pound) of each product. The best value for money is the product that gives the most produce per pound(/penny).

Example 1

Three bottles of the same sauce each have a different sized bottle with a different price, as shown:

bottle size	volume of sauce given	price
Small	$200ml$	$£3$
Medium	$450ml$	$£5.50$
Large	$1l$	$£12$

Which of the bottles gives the most value for money?

Work out how much sauce each bottle gives for $£1$ using ratios.

First, the small bottle:

$£3=200ml$ 

$£1=(200\div3)ml$ 

$£1=66.7ml$ 

The middle bottle:

$£5.50=450ml$

$£1=(450\div5.5)ml$

$£1=81.8ml$

The large bottle:

$£12=1l$

$£12=1000ml$

$£1=(1000\div12)ml$

$£1=83.3ml$

Hence, the large bottle is the best value for money as you get the most sauce per pound.