The students in three classes are in the rati | vedclass

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Question

(B) Let the original number of students in the three classes be $4x$,$6x$,and $9x$ respectively.According to the problem,when $12$ students are added

Vedclass · Accepted Answer

$76$

Vedclass · Answer

(B) Let the original number of students in the three classes be $4x$,$6x$,and $9x$ respectively.According to the problem,when $12$ students are added to each class,the new ratio becomes $7:9:12$.We can set up the equation using the first two classes: $\frac{4x + 12}{6x + 12} = \frac{7}{9}$.Cross-multiplying gives: $9(4x + 12) = 7(6x + 12)$.$36x + 108 = 42x + 84$.Rearranging the terms: $108 - 84 = 42x - 36x$.$24 = 6x$,which gives $x = 4$.The total number of students before the increase is $4x + 6x + 9x = 19x$.Substituting $x = 4$,we get $19 	imes 4 = 76$.

The students in three classes are in the ratio $4:6:9$. If $12$ students are increased in each class,the ratio changes to $7:9:12$. Then the total number of students in the three classes before the increase is

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