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

This isn't anything to do with the questions on this page... it's just an illustration!
This isn't anything to do with the questions on this page... it's just an illustration!

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?

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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Comments 2 comments

bla bla bla  6 years ago

hiya how do u work out 3000

x250

____

____


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EmpressFelicity 6 years ago from Kent, England, UK Author

Hi there bla bla bla, if you want to calculate 3000 x 250 without a calculator, you work out 3 x 25 (which is 75). Then add 4 zeros onto your answer (3 zeros from the 3000 and 1 from the 250). So your answer is 750,000. You can do this when you're multiplying any whole numbers that have zeros on the end. More to come in another hub, I think.

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