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If the sum between the smallest and largest of 5 consecutive odd numbers is 1,854, what is their positive difference?
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Answer to a math question If the sum between the smallest and largest of 5 consecutive odd numbers is 1,854, what is their positive difference?
Hermann
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Denotemos el más pequeño de los 5 números impares consecutivos como \( x \) . Como son números impares consecutivos, los otros cuatro números serían \( x + 2 \) , \( x + 4 \) , \( x + 6 \) , y \( x + 8 \) .
La suma de estos cinco números se da como 1.854:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 1854 \]
Combinando términos semejantes:
\[ 5x + 20 = 1854 \]
Restando 20 de ambos lados:
\[ 5x = 1834 \]
Dividiendo por 5:
\[ x = 366 \]
Entonces, los cinco números impares consecutivos son 366, 368, 370, 372 y 374.
La diferencia positiva entre el menor y el mayor de estos números es:
\[ 374 - 366 = 8 \]
Por tanto, la diferencia positiva entre el menor y el mayor de los 5 números impares consecutivos es 8.
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