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## 'Mixing More Paints' printed from http://nrich.maths.org/

This problem follows on from

Mixing Paints .

A decorator can buy pink paint from two manufacturers.

- Paint A is made up from red and white paint in the ratio
$1:4$
- Paint B is made up from red and white paint in the ratio
$1:5$

She can mix the paints to produce a different shade of pink.

What is the least number she would need of each type in order to
produce pink paint containing red and white in the following
ratios:

Another decorator buys pink paint from two different
manufacturers:

- Paint C is made up from red and white paint in the ratio
$1:3$
- Paint D is made up from red and white paint in the ratio
$1:7$

What is the least number she would need of each type in order
to produce pink paint containing red and white in the following
ratios:

Is it always possible to combine two paints made up in the ratios
$1:x$ and $1:y$ and turn them into paint made up in the ratio $a:b$
? Experiment with a few more examples.

Can you describe an efficient way of doing this?