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Question 988533: during the first semester the ratio of the number of students in art class to the number of students in gym class was 2:7, however the art classes were really small and the gym classes were so large so the principal changed students classes for second semester in second semester the ratio of the numbers of students in art class to the number of students in gym class was 5:4 if 75 students were in in art class second semester how many were in art class and gym class first semester
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! during the first semester the ratio of the number of students in art class to the number of students in gym class was 2:7, however the art classes were really small and the gym classes were so large so the principal changed students classes for second semester in second semester the ratio of the numbers of students in art class to the number of students in gym class was 5:4
if 75 students were in in art class second semester, how many were in art class and gym class first semester
:
Let x = the multiplier in the first semester
then
2x = no. of students in art class in 1st semester
7x = no. in gym class
:
Let y = the multiplier in the 2nd semester
then
5y = art class in the 2nd semester
4y = gym class students
We know
5y = 75 art students in the 2nd semester
y = 75/5
y = 15 is the multiplier
then
4(15) = 60 students in gym in the 2nd semester
therefore
75 + 60 = 135 total students
:
In 1st semester, same total number of students
2x + 7x = 135
9x = 135
x = 135/9
x = 15 is the multiplier in the 1st semester
therefore
2 * 15 = 30 art students in the 1st
7 * 15 = 105 gym students in the 1st
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