SOLUTION: The total number of students studying in an university is 35,000, if the certain years boys raises by 6% and girls by 4% the population will be 36760. What is the number of boys an

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Question 1001684: The total number of students studying in an university is 35,000, if the certain years boys raises by 6% and girls by 4% the population will be 36760. What is the number of boys and girls.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
b = number of boys
g = number of girls.

b + g = 35000

1.06b + 1.04g = 36760

1.06b is the number of boys plus 6% times the number of boys.
1.04g is the number of girls plus 4% times the number of girls.

6% is equal to 6/100 = .06
4% is equal to 4/100 = .04

you have 2 equations that need to be solved simultaneously.

they are:

b + g = 35000
1.06b + 1.04g = 36760

from the first equation, solve for b to get b = 35000 - g
replace b with 35000 - g in the second equation to get:

1.06*(35000 - g) + 1.04g = 36760
remove parentheses to get:
1.06*35000 - 1.06g + 1.04g = 36760
simplify to get:
37100 - .02g = 36760
subtract 37100 from both sides of the equation to get:
-.02g = 36760 - 37100
simplify to get:
-.02g = -340
divide both sides of the equation by -.02 to get:
g = -340 / -.02 = 17000

since b + g = 35000, then b must be equal to 35000 - 17000 = 18000

b = 18000
g = 17000
b + g = 18000 + 17000 = 35000 - correct.

1.06b + 1.04g = 19080 + 17680 = 36760 - correct.

solution is confirmed as good.

number of boys is 18000 and number of girls is 17000.