Question

a certain shade of blue is made by mixing 1.5 quarts of blue paint with 5 quarts of white paint. If you need a total of 16.25 gallons of this shade of blue paint, how much of each color should you mix​

Answer 1

we know the blue and white paints are on a 1.5 : 5 ratio, thus, if we have a total of 16.25 gallons of paint to be split along that ratio, we can simply divide 16.25 by (1.5+5) and distribute accordingly.

$\bf \cfrac{blue}{white}\qquad \stackrel{ratio}{1.5:5}\qquad \cfrac{1.5}{5}~\hspace{5em}\cfrac{1.5\cdot \frac{16.25}{1.5+5}}{5\cdot \frac{16.25}{1.5+5}}\implies \cfrac{1.5\cdot \frac{16.25}{6.5}}{5\cdot \frac{16.25}{6.5}} \\\\\\ \cfrac{1.5\cdot 2.5}{5\cdot 2.5}\implies \cfrac{3.75}{12.5}\qquad \qquad \boxed{\stackrel{blue}{3.75}~:~\stackrel{white}{12.5}}$