Let [tex]b[/tex] be the amount (in quarts) of blue paint used in the mix, and [tex]w[/tex] the amount of white paint. For the desired shade, there are 1.5 qt of blue paint for every 5 qt of white, so that [tex]1.5b=5w\implies w=0.3b[/tex].
1 gallon = 4 quarts, so 16.25 gal = 65 qt. We want this amount of the final mixed paint, so that [tex]b+w=65[/tex].
Subsituting [tex]w=0.3b[/tex] into this equation gives us
[tex]b+0.3b=1.3b=65\implies b=50[/tex]
so we need to use 50 qt of blue paint and 15 qt of white paint (since 65 - 50 = 15).
