Final Answer:
The correct volume of paint mixed by each boy is 23 quarts. Thus the correct option is 2.
Step-by-step explanation:
To find the volume of paint mixed by each boy, we need to assess the given options and identify the most plausible answer. It's important to note that the volume of paint cannot be negative, ruling out option 1 (-23 quarts). Option 2 (23 quarts) is the correct answer, as it aligns with the positive nature of volume measurements and is a reasonable quantity for a paint mixing scenario.
The mathematical reasoning behind this conclusion is based on the fact that volume is a scalar quantity, and negative values are not applicable in this context. Therefore, the only valid option for the volume of paint mixed by each boy is 23 quarts, aligning with option 2.
In summary, the correct interpretation and application of measurement principles, particularly the non-negativity of volume, lead us to the conclusion that each boy mixed 23 quarts of paint. This understanding ensures that the chosen option is not only mathematically sound but also conceptually accurate within the context of measuring paint volume.
Complete question:
Liam and Evan are mixing paint. Liam uses 2 quarts of yellow paint and adds 314 jars of blue paint. Evan uses 12 quarts of yellow paint and adds 512 jars of red paint. They end up with the same volume of paint.
Part A Which equation represents the situation?
2x+314x=12x+512x 2+314x=12+512x 2x+314y=12a+512b 2+512x=12+314x
Part B What volume of paint did each boy mix?
−23 quart 23 quart 112 quarts