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A 30-in. board is to be cut into two pieces so that one piece is two-thirds as long as the other piece. Check both lengths of the board.

User Karlos
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Final answer:

To determine the lengths of the two pieces of the board, we can set up a proportion using the given information and solve for the unknown lengths. The longer piece is 18 inches and the shorter piece is 12 inches.

Step-by-step explanation:

To solve this problem, we can set up a proportion using the given information. Let the length of the longer piece be x and the length of the shorter piece be (2/3)x. Since the total length of the board is 30 inches, we can write the equation: x + (2/3)x = 30. Combining like terms, we get (5/3)x = 30. Multiplying both sides by 3/5, we find x = 18 inches. Therefore, the longer piece is 18 inches and the shorter piece is (2/3)(18) = 12 inches.

User RjOllos
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