Question

An artist mixes 2 parts blue paint and 3 parts yellow paint to make green. How many parts blue paint should the artist mix with 12 parts yellow paint to get the same shade of green?

Answer 1

To maintain the same shade of green, the artist should mix 8 parts of blue paint with 12 parts of yellow paint, as the initial ratio is 2 parts blue to 3 parts yellow.

Step-by-step explanation:

To determine how many parts of blue paint the artist should mix with 12 parts of yellow paint to create the same shade of green, we use proportional reasoning based on the initial mix ratio provided. The original recipe for green paint is 2 parts blue to 3 parts yellow. This can be written as a ratio of blue to yellow paint, 2:3. To maintain the same shade of green, we keep the proportion of blue to yellow paint consistent when we increase the amount of yellow paint to 12 parts.

We set up a proportion where the ratio of blue paint (B) to yellow paint (12) is equivalent to the original ratio (2 parts blue to 3 parts yellow):

2 / 3 = B / 12

Multiplying both sides of the equation by 12 gives us:

2 / 3 × 12 = B

This simplifies to:

B = (2 × 12) / 3

B = 24 / 3

B = 8

Therefore, the artist should mix 8 parts of blue paint with 12 parts of yellow paint to achieve the same shade of green.