Final answer:
To maintain the initial mixture's ratio of 3:7 for red and white paint, approximately 0.43 cups of red paint should be added to one cup of white paint.
Step-by-step explanation:
The subject of the question is to determine how much red paint should be mixed with one cup of white paint to maintain the same ratio as the initial mixture of 3 cups of red paint to 7 cups of white paint. We start by understanding the initial ratio, which is 3:7 (red to white). To maintain this ratio for just one cup of white paint, we need to divide both parts of the ratio by 7. This gives us 3/7:1.
Now, to find how much red paint is needed for one cup of white paint, we calculate 3/7 of a cup. This means that approximately 0.43 cups (since 3 divided by 7 is around 0.4286) of red paint should be added to one cup of white paint to maintain the original mixture's color balance.