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(A) Let the initial number of students in the three classes be $2x$,$3x$,and $4x$ respectively.According to the problem,when $12$ students are added t

Vedclass · Accepted Answer

$162$

Vedclass · Answer

(A) Let the initial number of students in the three classes be $2x$,$3x$,and $4x$ respectively.According to the problem,when $12$ students are added to each class,the new ratio becomes $8:11:14$.We can set up the equation using the first two classes: $\frac{2x + 12}{3x + 12} = \frac{8}{11}$.Cross-multiplying gives: $11(2x + 12) = 8(3x + 12)$.$22x + 132 = 24x + 96$.$2x = 36$,which means $x = 18$.The total number of students in the beginning was $2x + 3x + 4x = 9x$.Substituting $x = 18$,we get $9 	imes 18 = 162$.

The number of students in three classes are in the ratio $2:3:4$. If $12$ students are increased in each class,this ratio changes to $8:11:14$. The total number of students in the three classes in the beginning was:

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