Final answer:
The new ratio of red to blue paint is calculated by determining the original amounts of red and blue in a 44-liter mixture with an 8:3 ratio. Upon adding an extra 8 liters of blue paint, the amounts become 32 liters of red and 20 liters of blue, simplifying to a new ratio of 8:5.
Step-by-step explanation:
The student's question asks us to calculate the new ratio of red to blue paint after an additional 8 liters of blue paint is added to an original mixture. The original ratio is 8:3, and the total original mix is 44 liters. First, we need to calculate the amounts of red and blue paint in the original mixture. We have a system of equations: 8x + 3x = 44, where x represents the common measure for each part of the ratio. Solving this gives us x = 4, thus there are 32 liters of red paint (8x) and 12 liters of blue paint (3x).
Upon adding the extra 8 liters of blue paint, the new volume of blue is 12 + 8 = 20 liters. The red paint remains the same at 32 liters. So, the new ratio of red to blue paint is 32:20, which can be simplified by dividing both numbers by 4 to get 8:5. Hence, the new ratio of red to blue paint is 8:5.