Question says that Isabelle is mixing red paint with blue paint to make purple paint.
She adds 3/10 of a fluid ounce of red to 11/16 fluid ounces of purple.
Now we need to find about how many fluid ounces of red will she need to make 3 fluid ounces of purple paint.
So let we need x fluid ounces of red color paint.
To find that we can setup ratio between quantity of red and pruple colour paints.
[tex]\frac{Red}{Purple}=\frac{\left(\frac{3}{10}\right)}{\left(\frac{11}{16}\right)}=\frac{x}{3}[/tex]
[tex]\frac{\left(\frac{3}{10}\right)}{\left(\frac{11}{16}\right)}=\frac{x}{3}[/tex]
[tex]\left(\frac{3}{10}\right)\cdot\left(\frac{16}{11}\right)=\frac{x}{3}[/tex]
[tex]\frac{48}{110}=\frac{x}{3}[/tex]
[tex]\frac{48}{110}\cdot3=x[/tex]
[tex]\frac{72}{55}=x[/tex]
Hence final answer is [tex]\frac{72}{55}[/tex] fluid ounce of red colour.
