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On January 25th, 80% pass, on January 31st, 75% pass, and on February 3rd, 85% pass. Determine the minimum percentage of integralists?

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Answer to a math question On January 25th, 80% pass, on January 31st, 75% pass, and on February 3rd, 85% pass. Determine the minimum percentage of integralists?

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Cristian

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116 Answers

Să presupunem că numărul total de întregiți este reprezentat de variabila $x$.

Pe 25 ianuarie trec 80% din numărul total de întregiți, ceea ce înseamnă că numărul de întregiți care trec este $0.8x$.

Pe 31 ianuarie trec 75% din numărul total de întregiți, ceea ce înseamnă că numărul de întregiți care trec este $0.75x$.

Pe 3 februarie trec 85% din numărul total de întregiți, ceea ce înseamnă că numărul de întregiți care trec este $0.85x$.

Pentru a determina procentul minim de întregiți, trebuie să găsim cea mai mică valoare comună (CMMD) a procentelor menționate mai sus.

Luând în considerare acești trei factori comuni ai întregiților, putem folosi formula $CMMD = \frac{x}{100}$, unde $x$ reprezintă procentul minim de întregiți care trec.

CMMD = \frac{x}{100} = \frac{0.8x}{100} = \frac{0.75x}{100} = \frac{0.85x}{100}

Pentru a găsi procentul minim de întregiți, putem găsi CMMDC-ul procentelor 80%, 75% și 85%. Putem face acest lucru prin simplificarea fracțiilor:

CMMD = \frac{x}{100} = \frac{0.8x}{100} = \frac{4}{5} \cdot \frac{x}{100} = \frac{3}{4} \cdot \frac{x}{100} = \frac{17}{20} \cdot \frac{x}{100}

Acum putem determina procentul minim de întregiți:

\frac{x}{100} = \frac{17}{20} \cdot \frac{x}{100} \Rightarrow 1 = \frac{17}{20} \Rightarrow \frac{20}{20} = \frac{17}{20} \Rightarrow \frac{3}{20} = \frac{x}{100} \Rightarrow x = \frac{3}{20} \cdot 100 = \frac{300}{20} = \frac{15}{1} = 15

Answer: Procentul minim de înegalități este de 15%.

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