Final answer:
The largest number of curtains that can be made from 75 yards of green fabric and 125 yards of white fabric, with each curtain being the same length and no fabric leftover, is 3 curtains. Each curtain will use 25 yards of green fabric and 25 yards of white fabric.
Step-by-step explanation:
To find the largest number of curtains that can be made without any leftover fabric, we need to calculate the greatest common divisor (GCD) of the two lengths of fabric. The GCD of 75 yards (green) and 125 yards (white) will tell us the longest length of curtain that can be made from both fabrics without any waste. To find the GCD of 75 and 125, we list the factors of each number and identify the largest factor that they have in common:
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- Factors of 75: 1, 3, 5, 15, 25, 75
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- Factors of 125: 1, 5, 25, 125
The largest common factor is 25 yards. Thus, each curtain will be 25 yards in length. Now, we divide the total amount of fabric by 25 to determine the number of curtains:
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- 75 yards of green fabric ÷ 25 yards per curtain = 3 curtains
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- 125 yards of white fabric ÷ 25 yards per curtain = 5 curtains
However, since both green and white fabric must be used for each curtain and there are fewer green curtains, the largest number of curtains that can be made is 3 curtains. Each curtain will use 25 yards of green fabric and 25 yards of white fabric.