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The sum of the third and fourth part of a number is equal to double the number decreased by 17. Find the number. R

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Answer to a math question The sum of the third and fourth part of a number is equal to double the number decreased by 17. Find the number. R

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Rasheed
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105 Answers
Sean \( x \) el número buscado.

1. La tercera parte de \( x \) es \( \frac{x}{3} \).
2. La cuarta parte de \( x \) es \( \frac{x}{4} \).
3. La suma de la tercera y la cuarta parte de \( x \) es \( \frac{x}{3} + \frac{x}{4} \).
4. El doble del número disminuido en 17 es \( 2x - 17 \).
5. La ecuación es:
\frac{x}{3} + \frac{x}{4} = 2x - 17
6. Encontramos un común denominador y resolvemos la ecuación:
\frac{4x + 3x}{12} = 2x - 17
\frac{7x}{12} = 2x - 17
Multiplicamos ambos lados por 12:
7x = 24x - 204
Simplificamos:
-17x = -204
x = \frac{204}{17}
x = 12

Por lo tanto, el número es:
x = 12

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