a paint color is made by mixing red and yellow paint. the ratio of red to yellow is 4 to 9. how many quarts of yellow paint must be used for 12 quarts of red? explain how you find your answer.
Set up a proportion, cross multiply, and solve for x.
4/9 = 12/x
To find out how many quarts of yellow paint must be used for 12 quarts of red paint, we need to use the given ratio of 4 to 9.
First, we calculate the ratio of yellow paint to red paint. Since the ratio of red to yellow is 4 to 9, the ratio of yellow to red can be determined by taking the reciprocal of this ratio. So, the ratio of yellow to red is 9 to 4.
Next, we set up a proportion based on the given information. Let x be the number of quarts of yellow paint needed.
4 quarts of red paint / 9 quarts of yellow paint = 12 quarts of red paint / x quarts of yellow paint
Using cross-multiplication, we can solve the proportion:
4x = 12 * 9
4x = 108
Dividing both sides of the equation by 4, we get:
x = 108 / 4
x = 27
Therefore, 27 quarts of yellow paint must be used for 12 quarts of red paint according to the given ratio.