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Olympiad workbook
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Olympiad workbook
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IOQM
Chapter
Basics of Mathematics

Olympiad workbook · IOQM · Basics of Mathematics

In a class, the total numbers of boys and girls are in the ratio 4:...

In a class, the total numbers of boys and girls are in the ratio 4:34: 3. On one day it was found that 8 boys and 14 girls were absent from the class and that the number of boys was the square of the number of girls. What is the total number of students in the class?

Correct answer

42

Step-by-step solution

Ratio is 4:34: 3 therefore Boys are 4 x Girls are 3 x  given (4x−8)=(3x−14)29x2+196−84x=4x−89x2−88x+204=0x=88±882−4×9×20418=2(22±222−9×51)9=2(22±5)9=2×279 or 2×179x=6 or 349\begin{aligned} & \text { given }(4 x-8)=(3 x-14)^2 \\ & 9 x^2+196-84 x=4 x-8 \\ & 9 x^2-88 x+204=0 \\ & x=\frac{88 \pm \sqrt{88^2-4 \times 9 \times 204}}{18} \\ & =\frac{2\left(22 \pm \sqrt{22^2-9 \times 51}\right)}{9} \\ & =\frac{2(22 \pm 5)}{9}=2 \times \frac{27}{9} \text { or } 2 \times \frac{17}{9} \\ & x=6 \text { or } \frac{34}{9} \end{aligned} 7x=427 x=42 or non integer ⇒42\Rightarrow 42 students
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