Q:

some girls and some boys are raising money for a trip to China. there was 40% girls. after two girls left and two boys came, there was 30% girls. what was the original amount of girls?

Accepted Solution

A:
For an instance, g represents the original amount of girls and b represents the original amount of boys.

Write an equation based on the problem
There was 40% girls, the equation will be
g = 40% (b + g) 
first equation

If two girls left and two boys came, there was 30% girls, the equation will be
g - 2 = 30%(b + 2 + g - 2)
second equation

Work on the first equation
To make it easier in calculation, change percent into decimals
g = 40% (b + g)  
g = 0.4(b + g)
g = 0.4b + 0.4g

Work on the second equation
Change percent into decimals and simplify the equation
g - 2 = 30%(b + 2 + g - 2)
g - 2 = 0.3(b + g)
g = 0.3b + 0.3g + 2

Solve the equation system by substitution method
g = g
0.4b + 0.4g = 0.3b + 0.3g + 2
0.1b + 0.1g = 2
0.1(b + g) = 2
b + g = 20
The original amount of boys and girls is 20

Find the original amount of girls
Original amount of girls is equal to 40% of the original amount of boys plus girls.
g = 0.4(b + g)
g = 0.4(20)
g = 8
The original amount of girls is 8