Final answer:
After mixing both glasses, the new ratio of vinegar to water is 9:31.
Step-by-step explanation:
To determine the new ratio of vinegar to water after mixing both glasses, we need to calculate the quantity of vinegar and water in each glass and then combine them. Let's assume the first glass has a capacity of 'V' units. In the first glass, with a vinegar to water ratio of 1:3, there is 1 part vinegar and 3 parts water. If 'V' is the total volume, then we have V/4 units of vinegar and 3V/4 units of water.
The second glass has twice the capacity, so it has a volume of '2V' units. The ratio in the second glass is 1:4, meaning it contains 2V/5 units of vinegar and 8V/5 units of water. When we mix the contents of both glasses, we get (V/4 + 2V/5) units of vinegar and (3V/4 + 8V/5) units of water.
The final step is to simplify this sum to get the resulting ratio.
Vinegar: V/4 + 2V/5 = (5V + 4V)/20 = 9V/20
Water: 3V/4 + 8V/5 = (15V + 16V)/20 = 31V/20
The new ratio of vinegar to water after mixing is therefore 9V/20 : 31V/20, which simplifies to 9:31.