Question

tN11. A certain shade of purple paint ismade using 1/3 cup of blue paint forevery 1/2 cup of red paint. How muchblue and red paint would be needed tomake 12 cups of this purple paint?S0

Answer 1

4.8cups of blue paint

7.2cups of red paint

Explanations:

If a certain shade of purple paint is made using 1/3 cup of blue paint for every 1/2 cup of red paint, the total combination of colours needed for one cup of the purple colour will be:

`\begin{gathered} =(1)/(3)c(blue)+(1)/(2)c(red) \\ =(2c+3c)/(6) \\ =(5)/(6)c\text{ of purple} \end{gathered}`

Note that the addition of blue and red is purple.

To get the amount of blue and red paint would be needed to make 12 cups of this purple paint, we will equate the result to 12 and find c as shown;

`\begin{gathered} (5)/(6)c=12 \\ 5c=6*12 \\ 5c=72 \\ c=(72)/(5) \\ c=14.4 \end{gathered}`

Get the amount of blue paint needed:

`\begin{gathered} \text{blue paint n}eeded=(1)/(3)c \\ \text{blue paint n}eeded=(1)/(3)*14.4 \\ \text{blue paint n}eeded=4.8\text{cups} \end{gathered}`

Get the amount of red paint needed:

This shows that 4.8cups of blue paint and 7.2cups of red paint is needed to make 12 cups of this purple paint