# How to calculate ratio part III: answers to problems in part II

__Problem 1__

*Stuart and Ali run a printing business together. When they started the business, Stuart put in £1,500 and Ali put in £2,500. What is the ratio of Ali's to Stuart's contribution, in its simplest form?*

The thing with this type of question is to make sure that you get the numbers in the right order. Since you're talking about the earnings ratio of Ali to Stuart, you put Ali's earnings first, which would give:

£2,500 : £1,500

Or, because you don't need the "£" signs when you're talking about ratios:

2,500 : 1,500

Then you need to cancel down, in stages if you find that easier. The obvious thing to do with this one would be to take the zeros off, which gives:

25 : 15

and then divide each side by 5, to give an answer of:

**5 : 3**

__Problem 2__

*Five years later Stuart and Ali decide to sell the business to a Mrs Khan. They split the proceeds (£24,000) in the same ratio as the ratio of their original contributions. How much does Ali get?*

Using the answer of 5:3 that you got in Problem 1, the total number of "parts" is

5 + 3 = 8. Each part is therefore worth £3,000 (£24,000 divided by 8).

So Ali gets 5 x £3,000 = **£15,000**

And Stuart gets 3 x £3,000 = **£9,000**

This is a "splitting ratio" type of question BTW.

__Problem 3__*To make Green Shimmer paint, you need to mix Yellow Sun, Blue Topaz and Silver Moon paints in a ratio of 7:7:4. How much of each colour do you need in ml if you're making 36 litres of Green Shimmer? Hint: 1 litre = 1,000 ml*

Like Problem 2, this is a "splitting ratio" type of question where you know how much final product you're making and you need to split it up into its individual parts. The total number of "parts" of paint is

7 + 7 + 4 = 18

Each part is worth 2 litres (36 divided by 18 = 2)

You need 7 x 2 = 14 litres of Yellow Sun (and 14 litres of Blue Topaz as well)

14 litres = 14 x 1,000 =

**14,000 ml**each of Yellow Sun and Blue Topaz

**and**

4 x 2 = 8 litres =

**8,000 ml**of Silver Moon.

You could have converted the 36 litres to 36,000 ml right from the outset and gone from there. Sometimes this is actually quite a good thing to do, as the answer to Problem 6 will hopefully demonstrate.

__Problem 4__

*Broadview Animal Rescue Centre has 270 dogs and 195 cats. What is the ratio of cats to dogs, expressed in its simplest form?*

The ratio of cats to dogs is

195 : 270

If it helps, do this one in stages. For example, you can divide both numbers by 3, giving

65 : 90

and then again by 5, giving

**13 : 18**as your answer

__Problem 5__

*When making chocolate cake, Andy needs a 5:3:2 weight ratio of flour, cocoa powder and caster sugar. If he uses 28 grams of sugar, how much of the other ingredients does he need?*

This isn't as hard as it seems. The 28 grams of sugar corresponds to two "parts". One part is therefore 28/2, or 14 grams.

The amount of flour is therefore 14 x 5 =

**70 grams**

And the amount of cocoa powder is 14 x 3 =

**42 grams.**

__Problem 6__

*Kylie is having a party and wants to make a punch bowl of Sea Breeze cocktail, which consists mainly of 2 parts vodka, 3 parts cranberry juice and 3 parts grapefruit juice. How much of each ingredient (in ml) would she need to make:*

a) 4 litres of cocktail

b) 1 litre of cocktail?

a) 4 litres of cocktail

b) 1 litre of cocktail?

The total number of parts of all the ingredients is 2 + 3 + 3 = 8

For (a), 8 = 4 litres, so each part = half a litre (or 0.5 litres if you're writing it as a decimal). If you're not comfortable working in fractions or decimals (and since you need to give the answer in ml anyway), at this point it's worth converting the 4 litres to ml, giving 4,000 ml.

8 parts = 4,000 ml

Therefore one part = 500 ml

Amount of vodka = 2 x 500 ml =

**1,000 ml**

Amount of cranberry juice = amount of grapefruit juice = 3 x 500 ml =

**1,500 ml**

For (b)

1 litre = 1,000 ml = 8 parts

Therefore 1 part = 1,000 divided by 8 = 125 ml

Amount of vodka = 2 x 125 ml =

**250 ml**

Amount of cranberry juice = amount of grapefruit juice = 3 x 125 ml =

**375 ml**

© Empress Felicity August 2010

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