The idea

Ratio problems where the amounts change

How to handle ratios where quantities are added, removed or transferred by writing the parts as multiples of a common number and solving for it.

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Ratio, proportion & rates of change · Ratio

How to handle ratios where quantities are added, removed or transferred by writing the parts as multiples of a common number and solving for it.

The hardest ratio questions give you a ratio before a change and a ratio after it — "the ratio of red to blue is

3 : 4

;

6

more red are added and it becomes

9 : 8

." You can't just work with

3

and

4

as if they were the real amounts, because there could be

3

and

4

, or

30

and

40

, or

300

and

400

— all in the ratio

3 : 4

. The trick is to write the unknown amounts as multiples of a single number:

\text{red} = 3k, \qquad \text{blue} = 4k,

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The rest of the explanation, plus 2 worked examples you step through move by move.

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