Question

This year a kindergarten class has 360 children, a 20% increase over last year. There was a 10% increase in the number of boys and a 40% increase in the number of girls. How many boys and girls were there each at the kindergarten class last year?

Answer 1

Set up your variables:
B1 = # of boys last year
B2 = # of boys this year
G1 = # of girls last year
G2 = # of girls this year

We know that B2 + G2 = 360
There was a 20% increase from last year in total students, so:
360/1.2 = 300 total students last year
So we have:
B1 + G1 = 300 (our first equation)

Now there was a 10% increase in boys, so:
1.1*B1 = B2
And 40% increase in grills, so:
1.4G1 = G2

So substituting these values into B2 + G2 = 360, gets us:
1.1*B1 + 1.4*G1 = 360 (our second equation)

Now we have two equations and two unknowns:
B1 + G1 = 300
1.1*B1 + 1.4*G1 = 360

I'll multiply the top equation by 11 and the bottom equation by 10:
11B1 + 11G1 = 3300
11B1 + 14G1 = 3600

Subtract the two equations:
-3G1 = -300
G1 = 100

Thus B1 must be 200.

There were 200 boys last year and 100 girls last year.