for that some problem: A board that is 12 feet long must be cut into 2 pieces that have lengths in a ratio of 3 to 2. Find the lengths of the two pieces. arn't you solving two parts because the board was cut in two?

Yes. I showed you the length of the longer piece. And then I told you to subtract it from 12 to find the length of the shorter piece.

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Yes, you are correct. The problem requires us to cut a 12-foot board into two pieces in a specific ratio. To find the lengths of the two pieces, we need to divide the board into two parts according to the given ratio.

To solve this problem, we can follow these steps:

Step 1: Determine the total ratio.
The total ratio is the sum of the ratio of the lengths. In this case, the ratio is 3:2, so the total ratio is 3 + 2 = 5.

Step 2: Calculate the length of one part.
To find the length of one part, divide the total length of the board by the total ratio.
Length of one part = (Total length of the board) / (Total ratio) = 12 ft / 5 = 2.4 ft

Step 3: Calculate the lengths of the two pieces.
Now that we know the length of one part is 2.4 feet, we can find the lengths of the two pieces by multiplying the length of one part by the respective ratios.
Length of the first piece = 2.4 ft * 3 = 7.2 ft
Length of the second piece = 2.4 ft * 2 = 4.8 ft

Therefore, the lengths of the two pieces are 7.2 feet and 4.8 feet, respectively.