Question

A certain shade of light blue is made by mixing 1 1/2 qrts of blue paint with 5 qrts of white paint. How much white paint would you need to mix with 4 qrts of blue paint

Answer 1

Compare the two ratios by turning them into fractions

`\begin{gathered} 1(1)/(2)\text{blue is to }5\text{ white}\Longrightarrow(1(1)/(2))/(5) \\ 4\text{ blue is to }x\text{ white}\Longrightarrow(4)/(x) \end{gathered}`

Equate the two and solve for the missing value

`\begin{gathered} (4)/(x)=(1(1)/(2))/(5) \\ \text{Get the reciprocal of both} \\ (x)/(4)=(5)/(1(1)/(2)) \\ (x)/(4)=(5)/(1.5) \end{gathered}`

Multiply both sides by 4 to get rid of the left side's denominator

`\begin{gathered} 4\mleft((x)/(4)=(5)/(1.5)\mright)4 \\ \cancel{4}\mleft(\frac{x}{\cancel{4}}=(5)/(1.5)\mright) \\ x=(5\cdot4)/(1.5) \\ x=(20)/(1.5) \\ x=13.333\ldots \\ \text{or when converted to mixed fraction} \\ x=13(1)/(3) \end{gathered}`

Therefore, you need 13 1/3 quarts of white paint.