Final answer:
The shortest length that Sam and Becky can achieve for their lines of 8-inch and 12-inch sticks, such that both lines are equally long, is 72 inches, by finding the least common multiple of 8 and 12.
Step-by-step explanation:
The question is asking for the shortest length of line that Sam and Becky can make using their sticks of 8 inches and 12 inches respectively, such that both lines are equally long. To solve this, we need to find the least common multiple (LCM) of the lengths of the two different sticks. The LCM of 8 and 12 is 24 inches, which is the shortest length that both sticks can make if laid end-to-end. However, we're looking for the shortest possible combined length, which will be a multiple of 24 inches.
So, we need to list the multiples of 24 and find the smallest one that is achievable with both 8-inch and 12-inch sticks. The multiples of 24 are: 24, 48, 72, 96, and so on. We can rule out 24 and 48 because they are not multiples of 8. The next multiple, 72, is a multiple of both 8 and 12 (8x9=72 and 12x6=72), so this is the smallest length where both lines can be equally long.
Thus, the shortest combined length of the lines that Sam and Becky can have, such that both of their lines are equally long, is 72 inches, which corresponds to answer choice D.