MATH SOLVE

2 months ago

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

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