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.