Question

Charlotte and Pablo are each making purple paint by mixing blue

paint and red paint. Charlotte uses 1 cup of red paint for every
2 cups of blue paint. Pablo uses 2 cups of red paint for every
3 cups of blue paint. Whose paint is a bluer shade of purple?

Answer 1

Charlotte's mix has a bluer shade of purple

Explanation:

Since we are asked whose paint is a bluer shade it would be easier to express the ratios of the paint mix as blue:red

Charlotte: 1 cup red for every 2 cups blue ==> 2 cups blue for every 1 cup red

This can be expressed as the ratio

`( 2 \;blue)/(1\;red) = (2)/(1) = 2`

`-------------------`

Pablo : 2 cups red for every 3 cups blue ==> 3 cups blue for every 2 cups red

The ratio of blue to red
=
`(3 \;blue)/(2\;red) = (3)/(2) = 1(1)/(2) \;\; (or\; 1.5)`

Since

`2 > 1(1)/(2) \;\;\;(or\; 2 > 1.5)`

Charlotte's mix has a bluer shade of purple