Question

the number of student in 3 room is 138 the ratio of the number of student in room 1 and 2 is 3/4and room to and 3 is 7/5 find the first number of student in the first room ​

Answer 1

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Answer 2

The number of student in the first room​ is 42

Solution:

Let the number of students in room 1 = x

Let the number of students in room 2 = y

Let the number of students in room 3 = z

Then,

The ratio of the number of student in room 1 and 2 is 3/4

$\frac{x}{y} = \frac{3}{4}\\\\x = \frac{3y}{4}$

The ratio of the number of student in room 2 and 3 is 7/5

$\frac{y}{z} = \frac{7}{5}\\\\z = \frac{5y}{7}$

Total number of students = 138

Thus,

$x + y + z = 138 \\\\\frac{3y}{4} + y + \frac{5y}{7} = 138 \\\\\frac{21y + 28y + 20y}{28} = 138\\\\69y = 138 \times 28\\\\\ y = 56$

Thus,

$x = \frac{3y}{4} \\\\x = \frac{3 \times 56 }{4} \\\\x = 42$

Thus number of student in the first room​ is 42

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