Mixing Paints

A decorator can buy pink paint from two manufacturers.

Paint A is made up from red and white paint in the ratio $1:3$
Paint B is made up from red and white paint in the ratio $1:7$

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

If Paint A and Paint B come in same size cans, what is the least number he would need of each type in order to produce pink paint containing red and white in the following ratios:

$1:4$
$1:5$
$1:6$

Another decorator buys pink paint from two different manufacturers:

Paint C is made up from red and white paint in the ratio $1:4$
Paint D is made up from red and white paint in the ratio $1:9$

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

$1:5$
$1:6$
$1:7$
$1:8$

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 $1:z$ ? (where $x < z < y$)

Experiment with a few more examples.

Can you describe an efficient way of doing this?

Mixing More Paints is a follow-up question to this one.