Jenna had 24.5 yards of lace. She cut it into pieces of equal length between 2 and 4 yards long. The pieces are multiples of 0.5 yard in length.
How long is each piece?
How many pieces does she have?
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Between 2 and 4 yards, and
A multiple of 0.5.
No integer can be the answer, because it wouldn't divide evenly into 24.5.
The only two possibilities are then 2.5 and 3.5. Which is it?
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To find the length of each piece, we know that the pieces are multiples of 0.5 yards in length and each piece is between 2 and 4 yards long.
To determine the possible lengths of each piece, we can start by finding the multiples of 0.5 within the range of 2 to 4.
Multiples of 0.5 within the range of 2 to 4 are:
2.0, 2.5, 3.0, and 3.5.
Therefore, the possible lengths of each piece are 2.0, 2.5, 3.0, and 3.5 yards.
Now, let's calculate the number of pieces Jenna has.
To find the number of pieces, we can divide the total length of lace Jenna has (24.5 yards) by the length of each piece.
For each length of piece (2.0, 2.5, 3.0, and 3.5), we can calculate the number of pieces by dividing 24.5 by the length of each piece:
Number of pieces for 2.0 yards = 24.5 / 2.0
Number of pieces for 2.5 yards = 24.5 / 2.5
Number of pieces for 3.0 yards = 24.5 / 3.0
Number of pieces for 3.5 yards = 24.5 / 3.5
Performing these calculations, we get:
Number of pieces for 2.0 yards = 12.25 pieces
Number of pieces for 2.5 yards = 9.8 pieces
Number of pieces for 3.0 yards = 8.17 pieces
Number of pieces for 3.5 yards = 7 pieces
Since the number of pieces must be a whole number, we can round down all the partial pieces to the nearest whole number:
Number of pieces for 2.0 yards = 12 pieces
Number of pieces for 2.5 yards = 9 pieces
Number of pieces for 3.0 yards = 8 pieces
Number of pieces for 3.5 yards = 7 pieces
Therefore, each piece can be either 2.0, 2.5, 3.0, or 3.5 yards long, and Jenna has 12, 9, 8, or 7 pieces, respectively.