To maintain the ratio of blue paint to red paint as 4:6, you can first find the common factor between 4 and 6, which is 2.
Then, you can simplify the ratio by dividing both parts by 2:
4/2 = 2
6/2 = 3
So, the simplified ratio is 2:3.
Now, you know that for every 2 parts of blue paint, you need 3 parts of red paint. Given that the painter is using 200 gallons of blue paint, you can calculate the amount of red paint required.
Divide the 200 gallons of blue paint into 2 parts:
200 / 2 = 100
Now, for every 2 parts of blue paint, you need 3 parts of red paint. So, for 200 gallons of blue paint, you would need:
3 parts (red paint) * 100 = 300 gallons of red paint.
The painter should use 300 gallons of red paint to maintain the 4:6 ratio and create the perfect color purple.