SOLUTION: Solve the following problem 1. In a particular school, the number of girls varies directly as the number of boys and inversely as the number of teachers. When there were 40 girls,

Question 1175781: Solve the following problem
1. In a particular school, the number of girls varies directly as the number of boys and inversely as the number of teachers. When there were 40 girls, there where 25 teachers and 10 boys. how many boys were there 30 girls and 60 teachers?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
direct variation formula is g = k * b / t.
g is the number of girls.
b is the number of boys.
t is the number of teachers.

you are given that g = 40 when t = 25 and b = 10.
the formula becomes 40 = k * 10 / 25
solve for k to get k = 40/10 * 25 = 100
that's your constant of variation.
it is used to solve for one of the other variables in the eqution when two of the other variables are known.
when there were 30 girls and 60 teachers, the formula becomes 30 = 100 * b / 60
solve for b to get 30 * 60 / 100 = 1800 / 100 = 18.
that's your solution.

when there are 40 girls and 25 teachers, there are 10 boys.
when there are 30 girls and 60 teachers, there are 18 boys.

solve for the number of boys in both equations to see if the constant of variation is correct.
40 = 100 * b / 25.
solve for b to get b =25 * 40 / 100 = 1000 / 100 = 10
30 = 100 * b / 60.
solve for b to get b = 60 * 30 / 100 = 1800 / 100 = 18.

the constant of variation is good.
your solution is b = 18 when t = 60 and g = 30.

here is a reference on variation formulas.

https://www.purplemath.com/modules/variatn.htm

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