Compare the two ratios by turning them into fractions
[tex]\begin{gathered} 1\frac{1}{2}\text{blue is to }5\text{ white}\Longrightarrow\frac{1\frac{1}{2}}{5} \\ 4\text{ blue is to }x\text{ white}\Longrightarrow\frac{4}{x} \end{gathered}[/tex]
Equate the two and solve for the missing value
[tex]\begin{gathered} \frac{4}{x}=\frac{1\frac{1}{2}}{5} \\ \text{Get the reciprocal of both} \\ \frac{x}{4}=\frac{5}{1\frac{1}{2}} \\ \frac{x}{4}=\frac{5}{1.5} \end{gathered}[/tex]
Multiply both sides by 4 to get rid of the left side's denominator
[tex]\begin{gathered} 4\mleft(\frac{x}{4}=\frac{5}{1.5}\mright)4 \\ \cancel{4}\mleft(\frac{x}{\cancel{4}}=\frac{5}{1.5}\mright) \\ x=\frac{5\cdot4}{1.5} \\ x=\frac{20}{1.5} \\ x=13.333\ldots \\ \text{or when converted to mixed fraction} \\ x=13\frac{1}{3} \end{gathered}[/tex]
Therefore, you need 13 1/3 quarts of white paint.
