Question

En la Euler Middle School, $198$ estudiantes votaron sobre dos cuestiones en un referéndum escolar con los siguientes resultados: $149$ votaron a favor de la primera cuestión y $119$ votaron a favor de la segunda cuestión. Si hubo exactamente $29$ estudiantes que votaron en contra de ambas cuestiones, ¿cuántos estudiantes votaron a favor de ambas cuestiones?

At Euler Middle School, $198$ students voted on two issues in a school referendum with the following results: $149$ voted in favor of the first issue and $119$ voted in favor of the second issue. If there were exactly $29$ students who voted against both issues, how many students voted in favor of both issues?

$49$

$70$

$79$

$99$

$149$

Solución en video:

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Solución escrita:

Como $29$ estudiantes votaron en contra de ambas, sabemos que $198-29 = 169$ personas votaron a favor de al menos una.

Como sabemos que $149$ estudiantes votaron a favor de la primera cuestión, $119$ estudiantes votaron a favor de la segunda, y $169$ estudiantes votaron a favor de al menos una, concluimos que el número de estudiantes que votaron a favor de ambas es $149+119-169 = 99.$

Por lo tanto, la respuesta correcta es D.

Since $29$ students voted against both, we know that $198-29 = 169$ people voted for at least one.

As we know that $149$ students voted for the first issue, and $119$ students voted for the second issue, and $169$ students that voted for at least one issue, we conclude that the number of students that voted for both is $149+119-169 = 99.$

Thus, the correct answer is D .

2015 AMC 8 Problema 15

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El Problema 15 en otros años