Answer: 9 gallons
Step-by-step explanation:
Given: Ratio of colors in painting:
4 parts blue, 3 parts red, and 3 parts green.
Total parts = 4+3+3 =10
Fraction of blue = ![\dfrac{\text{Number of parts of blue}}{\text{total parts}}=\dfrac{4}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BNumber%20of%20parts%20of%20blue%7D%7D%7B%5Ctext%7Btotal%20parts%7D%7D%3D%5Cdfrac%7B4%7D%7B10%7D)
Since, Quantity of blue color used = 12 gallons
Let total quantity of color be x,
![\dfrac{4}{10}x=12\\\\\Rightarrow\ x=\dfrac{120}{4}=30\text{ gallons}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B10%7Dx%3D12%5C%5C%5C%5C%5CRightarrow%5C%20x%3D%5Cdfrac%7B120%7D%7B4%7D%3D30%5Ctext%7B%20gallons%7D)
Total color used = 30 gallons
Color used for green part only = ![\dfrac{3}{10}\times30 = \text{9 gallons}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B10%7D%5Ctimes30%20%3D%20%5Ctext%7B9%20gallons%7D)
Hence, 9 gallons of paint were needed for the green part of the painting.