Final answer:
The patterns will line up every 12 inches, so we must find the first multiple of 12 among the given options. The correct answer is 114 inches, as it is a multiple of 12 (12 x 9.5 = 114).
Step-by-step explanation:
The question involves finding when two patterns that repeat at a different rate will align again. One pattern repeats every 12 inches. To find when two such patterns will line up again, we look for the least common multiple (LCM) of the repeating distances. Since we have only one repeating distance of 12 inches, the patterns will line up every 12 inches. Therefore, the first option we encounter that is a multiple of 12 inches is the correct answer.
The design is 19 feet long, but this piece of information is not needed to find when the patterns will line up again, since that depends solely on the repeating interval of the pattern.
The possible answers are: A) 38 inches, B) 57 inches, C) 76 inches, D) 114 inches. Checking each option, we see that 114 is the first one that is a multiple of 12 (12 x 9.5 = 114) and hence is the correct answer.