The ratio of red to blue in a purple dye is 2 : 3. How many parts of blue need to be added to change the dye to 80% blue?

Question

4. The ratio of red to blue in a purple dye is 2 : 3. How many parts of blue need to be added to change the dye to 80% blue?

Answer 1

Let b be the number of parts of blue dye to be added. Initially the total number of parts of the purple mixture is 2+3=5, that is, 2/5 red, 3/5 blue. After adding b parts of blue we have 80% blue and therefore 20% red. The ratio of blue to red changes to 80/20=4.

So blue/red initially = 3/2 and (3+b)/2=4, 3+b=8, b=8-3=5 parts, to be added to make a bluer purple.

CHECK

After adding 5 parts of blue dye we get 5+3=8 parts of blue dye but still only 2 of red, ratio of blue to red changes to 4, and the the total number of parts in the purple mixture is 10, 8/10 (80%) blue, 2/10 (20%) red.