What is the number of female students this year?

Question

Last year the number of students in a school was 750. This year the number of male students has decreased by 9% , whereas the number of female students has increased by 20% . The net change in students is an increase of 34 . What is the number of female students this year?

Answer 1

Let x = number of female students originally and let y = number of male students originally.

 

 

 

There were originally 750 students in the school. So:

 

x + y = 750

 

The number of males decreased by 9%. So, the school lost a total of 0.09y male students. The number of females increased by 20%. So, the school gained a total of 0.2x female students. Since the student population increased by 34 overall:

 

0.2x - 0.09y = 34

 

 

 

Now you have a system of two equations:

 

x + y = 750

0.2x - 0.09y = 34

 

Solve the first equation for y, then plug that into the second equation to solve for x:

 

y = 750 - x

 

0.2x - 0.09y = 34

0.2x - 0.09(750 - x) = 34

0.2x - 67.5 + 0.09x = 34

0.29x - 67.5 = 34

0.29x = 101.5

x = 350

 

That means there were x = 350 students originally. Since the female students increased by 20%, there are currently 1.2(350) = 420 female students at the school.

Answer 2

Lets let M = # Males last year

            F = # Females last year

            We know then that  M + F = 750

 

This year we have a decrease of 9% in the males so we have 91% as many males or .91M this year

This year we have an increase of 20% in the females so we have 120% as many females or 1.2F this year

Since the net total this year is 34 more total students we have .91M + 1.2F = 750 + 34

 

This gives us two simultaneous equations to solve

 

M+F = 750

.91M + 1.2F = 784

 

Solve for M in the 1st equation

M = 750 - F

Substitute that in place of M in the 2nd equation

 

.91(750-F) + 1.2F = 784

682.5 -.91F + 1.2F = 784

682.5 + .29F = 784

.29F = 784 - 682.5

.29F = 101.5

F = 101.5/.29

F = 350

 

Last year we had 350 females

This year we have 1.2(F) females or 1.2(350) = 420 female students