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We received several incorrect solutions like the ones below:
Combining paints A ($1:4$) and B ($1:5$):
Required
Ratio
|
Amount of
paint A
|
Amount of
paint B
|
$2:9$ | $1$ | $1$ |
$3:14$ | $1$ | $2$ |
$10:43$ | $7$ | $3$ |
Required
Ratio
|
Amount of
paint C
|
Amount of
paint D
|
$2:9$ | $5$ | $3$ |
$3:14$ | $7$ | $5$ |
$10:43$ | $27$ | $13$ |
To start off, we first need to know the fact that the mixing of $2$ paints essentially gives us the average of the two ratios. Eg; mixing $1:2$ and $1:5$ gives us $1:3,$ which is $\dfrac{\frac13+\frac16}2.$
So, let: