SOLUTION: The ratio of girls to boys in a mixed school is 5:6 on a raining day1/6 of the girls and 1/4 of the boys were absent .if the total no of the pupils that day was 390 how many of the

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of girls to boys in a mixed school is 5:6 on a raining day1/6 of the girls and 1/4 of the boys were absent .if the total no of the pupils that day was 390 how many of the      Log On


   

Question 1002647: The ratio of girls to boys in a mixed school is 5:6 on a raining day1/6 of the girls and 1/4 of the boys were absent .if the total no of the pupils that day was 390 how many of the pupil were boys?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = the number of boys
Let +g+ = the number of girls
---------------------------
(1) +g%2Fb+=+5%2F6+
(1) +g+=+%285%2F6%29%2Ab+
and
(2) +%285%2F6%29%2Ag+%2B+%283%2F4%29%2Ab+=+390+
multiply both sides by +12+
(2) +10g+%2B+9b+=+4680+
------------------------
By substitution:
(2) +10%2A%285%2F6%29%2Ab+%2B+9b+=+4680+
Multiply both sides by +6+
(2) +50b+%2B+54b+=+28080+
(2) +104b+=+28080+
(2) +b+=+270+
270 of the students were boys
and
(1) +g+=+%285%2F6%29%2Ab+
(1) +g+=+%285%2F6%29%2A270+
(1) +g+=+225+
check:
(2) +%285%2F6%29%2Ag+%2B+%283%2F4%29%2Ab+=+390+
(2) +%285%2F6%29%2A225+%2B+%283%2F4%29%2A270+=+390+
Multiply both sides by 12
(2) +10%2A225+%2B+9%2A270+=+4680+
(2) +2250+%2B+2430+=+4680+
(2) +4680+=+4680+
OK