SOLUTION: There are 152 students in 5th grade. 1/11 of the boys and 5 girls join a science club. In the rest of the students, boys and girls are equal. How many boys vs girls are in 5th grad

Question 1163629: There are 152 students in 5th grade. 1/11 of the boys and 5 girls join a science club. In the rest of the students, boys and girls are equal. How many boys vs girls are in 5th grade?
Found 3 solutions by Theo, ankor@dixie-net.com, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = number of boys
y = number of girls
x + y = 152
1/11 * x + 5 = s = number of students in the science club.
the rest of the boys and girls are equal in number each.
this means that 10/11 * x = y - 5
this is because x - 1/11 * x = 10/11 * x are the number of boys remaining and y - 5 are the number of girls remaining.
since they are equal, 10/11 * x = y - 5
solve for y to get:
y = 10/11 * x + 5
since x + y = 152, replace y with 10/11 * x + 5 to get:
x + 10/11 * x + 5 = 152
combine like terms to get:
21/11 * x + 5 = 152
subtract 5 from both sides of the equation to get:
21/11 * x = 147
multiply both sides of the equation by 11/21 to get:
x = 147 * 11 / 21 = 77
since x + y = 152, then y must be equal to 75 because 77 + 75 = 152.
you have:
x + y = 152 becomes 77 + 75 = 152 which is true
1/11 of the boys = 1/11 * 77 = 7
7 of the boys are in the science club.
the remaining number of boys is 77 - 7 = 70 who are not in the science club.
5 of the girls are in the science club.
the remaining number of girls is 75 - 5 = 70 who are not in the science club.
the number of boys and girls who are not in the science club are the same.
problem is solved.
solution is there are 77 boys and 75 girls in the 5th grade for a total of 152 students.

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
There are 152 students in 5th grade.
b + g = 152
1/11 of the boys and 5 girls join a science club. In the rest of the students, boys and girls are equal.
b - b = g - 5
b = g - 5
b - g = -5
use elimination
b - g = -5
b + g = 152
--------------------Adding eliminates g, find b
b = 147
21b = 147*11
21b = 1617
b = 1617/21
b = 77 boys
then
152-77 = 75 girls

How many boys vs girls are in 5th grad.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
There are 152 students in 5th grade. 1/11 of the boys and 5 girls join a science club. In the rest of the students, boys and girls are equal. How many boys vs girls are in 5th grade?

Let number of boys be B
Then number of girls = 152 - B
If of the boys joined the science club, then number of boys left =
If 5 girls joined the science club, then number of girls left = 152 - B - 5 = 147 - B
Since remaining sets are equal, we can then say that:
10B + 11B = 11(147) ------ Multiplying by LCD, 11
21B = 11(147)
Number of boys in the 5th grade, or
Number of girls? You should be able to find this!
N.B. You DON'T need to use all those variables that the other people used. It's UNNECESSARY, makes the problem more complicated, and can possibly lead to many mistakes!
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