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Mixing Paints

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

We received several incorrect solutions...

They were based on the misconception that the 'parts' in the ratios were of equal size and that you could add the ratios to work out the necessary combinations. 

However, one can of paint A (ratio 1:3) and one can of paint B (ratio 1:7) does not produce paint in the ratio 2:10 (or 1:5), since that would require that the one part red in can A has the same volume as the one part red in can B. This can't be the case since there are 4 parts in can A and 8 parts in can B, so 1/4 of can A is red and 1/8 of can B is red.

To compare equal quantitities we will need to express the ratio of the colours in can A as 2:6, so we have:

in can A: 2/8 red and 6/8 white,
in can B: 1/8 red and 7/8 white.

Combining one can of each paint will now give us

3/16 red and 13/16 white,

that is, paint in the ratio 3:13.

We did received two correct solutions from students at St Albans High School:

Click here to see Anjali's solution and here to see Lydia's solution.

We also received this algebraic approach from Jennifer, from NLCS Jeju in Korea.