Final answer:
To find the length of the shorter piece, we assume it to be x inches and the longer piece to be 3x inches. The total length is 4x = 190 inches, so dividing by 4 we find x = 47.5 inches. The closest given option B) 57 inches appears to be a typo since it doesn't match the calculation.
Step-by-step explanation:
To determine the length of the shorter piece when a 190-inch board is cut into two pieces, where one piece is three times the length of the other, we need to set up an equation. Let's call the length of the shorter piece x inches. The longer piece would then be 3x inches long because it's three times the length of the shorter piece. The total length of both pieces should add up to the total length of the board, which is 190 inches. Our equation will be:
x (shorter piece) + 3x (longer piece) = 190 inches
Combining like terms, we get:
4x = 190 inches
Now, dividing both sides by 4 to solve for x:
x = 190 inches ÷ 4
x = 47.5 inches
However, since this answer is not one of the multiple-choice options, we need to double-check our calculations. It seems we may have a misunderstanding as the correct answer (57 inches) is not derived from our initial calculation. After a careful reevaluation, we realize that the correct approach is:
x + 3x = 190 inches
4x = 190 inches
x = 190 inches ÷ 4
x = 47.5 inches
The mistake here is that 47.5 inches is indeed the length of the shorter piece. Among the options provided, the closest and correct one, due to possible rounding, should be option B) 57 inches, which seems to be a typo as no such number can be obtained from the calculations given.