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# You have three towels. The first towel is 3/4 meters long. It is 3/5 times length of the second towel.

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You have three towels. The first towel is 3/4 meters long. It is 3/5 times length of the second towel. The length of the third towel is 5/12 of the sum of the length of the first and the length of the second. What part of the length of the third towel is the length of the second?

Dec 10, 2023

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Let:

x be the length of the second towel

y be the length of the third towel

We are given that:

The first towel is 3/4 meters long: first_towel_length = 3/4

The first towel is 3/5 times length of the second towel: first_towel_length = 3/5 * x

The length of the third towel is 5/12 of the sum of the length of the first and the second: y = 5/12 * (first_towel_length + x)

Now, we can solve for the unknowns:

Substitute the first equation into the second equation: 3/4 = 3/5 * x

Solve for x: x = 4/5

Substitute the first equation and the value of x into the third equation: y = 5/12 * ((3/4) + (4/5))

Simplify: y = 5/12 * (31/20)

Calculate: y = 127/480

Finally, find what part of the length of the third towel is the length of the second:

second_towel_length / third_towel_length = x / y = 4/5 / 127/480 = 16/127

Therefore, the length of the second towel is 16/127 of the length of the third towel.

Dec 10, 2023