Question

Cee-Lo Green decided to paint his entire house purple! The purple paint mixture contains 1/2

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.