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1. tratemos de racionalizar el número decimal<img src="https://tex.z-dn.net/?f=0.52%5Coverline%7B27%7D%3D0.52%2B0.00%5Coverline%7B27%7D%5C%5C%20%5C%5C%5C%5C0.52%5Coverline%7B27%7D%3D0.52%2B0.%5Coverline%7B27%7D%5Cdiv100%5C%5C%20%5C%5C%5C%5C0.

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Dayanna45
5

1. tratemos de racionalizar el número decimal<img src="https://tex.z-dn.net/?f=0.52%5Coverline%7B27%7D%3D0.52%2B0.00%5Coverline%7B27%7D%5C%5C%20%5C%5C%5C%5C0.52%5Coverline%7B27%7D%3D0.52%2B0.%5Coverline%7B27%7D%5Cdiv100%5C%5C%20%5C%5C%5C%5C0.52%5Coverline%7B27%7D%3D%5Cdfrac%7B52%7D%7B100%7D%2B%5Cdfrac%7B27%7D%7B99%7D%5Ctimes%5Cdfrac%7B1%7D%7B100%7D%5C%5C%20%5C%5C%20%5C%5C0.52%5Coverline%7B27%7D%3D%5Cdfrac%7B1%7D%7B100%7D%5Cleft%2852%2B%5Cdfrac%7B27%7D%7B99%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%5C%5C0.52%5Coverline%7B27%7D%3D%5Cdfrac%7B1%7D%7B100%7D%5Cleft%2852%2B%5Cdfrac%7B3%7D%7B11%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%5C%5C%5C%5C0.52%5Coverline%7B27%7D%3D%5Cdfrac%7B1%7D%7B100%7D%5Ctimes%5Cdfrac%7B575%7D%7B11%7D%5C%5C%20%5C%5C%20%5C%5C%5C%5C0.52%5Coverline%7B27%7D%3D%5Cdfrac%7B575%7D%7B1100%7D" />2.

Ahora traduzcamos el problema<img src="https://tex.z-dn.net/?f=%5Cdfrac%7B4k%2B11%7D%7B11k%2B11%7D%3D%5Cdfrac%7B575%7D%7B1100%7D" />3.

Resolvamos<img src="https://tex.z-dn.net/?f=%5Cdfrac%7B4k%2B11%7D%7B11k%2B11%7D%3D%5Cdfrac%7B575%7D%7B1100%7D%3D%5Cdfrac%7B23%7D%7B44%7D%3D%5Cdfrac%7B23r%7D%7B44r%7D%5C%5C%20%5C%5C%5C%5C4k%2B11%3D23r%5Cwedge%2011k%2B11%3D44r%5C%5C%20%5C%5C4k%2B11%3D23r%5Cwedge%20k%2B1%3D4r%5C%5C%20%5C%5C4k%2B11%3D23r%5Cwedge%20k%3D4r-1%5C%5C%5C%5C4%284r-1%29%2B11%3D23r%5Cwedge%20k%3D4r-1%5C%5C%5C%5Cr%3D1%5C%5C%20%5C%5C%5C%5C%5Ctext%7BEntonces%20la%20fracci%5C%27on%20es%3A%20%7D%5Cdfrac%7B23%7D%7B44%7D" /> 4.

Respuesta 21.