Question

Cee-Lo Green decided to paint his entire house purple! The purple paint mixture contains 1/2
cup of blue paint and 1/3 cup of red paint. If you want to mix blue and red paint together in the
same ratio to make 20 cups of purple paint, how many cups of red and blue paint would you
need?

Answer 1

Answer

Find out the how many cups of red and blue paint would you  need .

To prove

As given

Cee-Lo Green decided to paint his entire house purple .

The purple paint mixture contains $\frac{1}{2}$cup of blue paint and  $\frac{1}{3}$ cup of red paint.

Thus the ratio of the blue paint to the red paint is given by.

$\frac{Blue\ paint}{Red\ paint} = \frac{\frac{1}{2}}{\frac{1}{3}}$

Thus

$\frac{Blue\ paint}{Red\ paint} = \frac{3}{2}$

As given

same ratio to make 20 cups of purple paint .

Let us assume that the x be the scalar multiple of the blue and the red paint.

Blue paint cups = 3x

Red paint cups = 2x

2x + 3x = 20

5x = 20

$x = \frac{20}{5}$

x = 4

Thus

Blue paint cups = 3 × 4

                        = 12 cups

Red paint cups = 2 × 4

                        = 8 cups

Therefore  8 cups of red and 12 cupsblue paint would you  need to form 20 cups of the purple paint.