SOLUTION: In a school of 600 students the number of boys is 360.when 60 new students are admitted in the school the ratio of the number of boys to the number of girls became 13:9. find the n

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a school of 600 students the number of boys is 360.when 60 new students are admitted in the school the ratio of the number of boys to the number of girls became 13:9. find the n      Log On


   

Question 740765: In a school of 600 students the number of boys is 360.when 60 new students are admitted in the school the ratio of the number of boys to the number of girls became 13:9. find the number of newly admitted boys..?
Found 3 solutions by lynnlo, ikleyn, greenestamps:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53567) About Me  (Show Source):
You can put this solution on YOUR website!
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In a school of 600 students the number of boys is 360. when 60 new students are admitted in the school
the ratio of the number of boys to the number of girls became 13:9. find the number of newly admitted boys ?
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Originally, were there 600 students in the school, 360 boys and 600-360 = 240 girls.

60 new students were admitted.

Let x be the number of boys among these 60; then the number of girls among these 60 was (60-x).


Now the number of boys is 360+x; the number of girls is 240 + (60-x) = 300-x.


We make the ratio according to the problem

    %28360%2Bx%29%2F%28300-x%29 = 13%2F9.


To find 'x', cross multiply, then simplify

    9*(360+x) = 13*(300-x),

    9*360 + 9x = 13*300 - 13x

    9x + 13x = 13*300 - 9*360

       21x   =      660

         x   =       660/21 = 30.


ANSWER.  30 boys were newly admitted.


CHECK.  %28360%2B30%29%2F%28300-30%29 = 390%2F270 = 13%2F9.   ! correct !

Solved.



Answer by greenestamps(13292) About Me  (Show Source):
You can put this solution on YOUR website!


The original number of students was 600. After 60 new students are admitted, the total number of students is 660.

The resulting ratio of boys to girls is 13:9.

Let 13x = new number of boys
Let 9x = new number of girls

13x+9x = 660
22x = 660
x = 30

The new number of boys is 13x = 390.

The original number of boys was 360.

The number of new boys admitted was 390-360 = 30.

ANSWER: 30 new boys