duke's counter dc

duke's counter dc

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Increasing \( x \) by 25% gives \( x + 0.25x = 1.25x \).Given \( 1.25x = 125 \).Solving for \( x \): \( x = \frac{125}{1.25} = 100 \).If the sum of the first \( n \) natural numbers equals 55, what is \( n \)?The sum of the first \( n \) natural numbers is \( \frac{n(n+1)}{2} \).Setting this equal to 55: \( \frac{n(n+1)}{2} = 55 \).Multiplying by 2: \( n(n+1) = 110 \).Solving \( n^2 + n - 110 = 0 \) using the quadratic formula, \( n = \frac{-1 \pm \sqrt{1 + 440}}{2} = \frac{-1 \pm 21}{2} \).Positive solution: \( n = 10 \).The perimeter of a rectangle is 60 meters, and its length is 5 meters more than twice its width. What is the width?