# Boys and girls 2

The ratio of boys to girls in the math club is 4:3 . After eight more girls join the club, the ratio becomes 1:1. How many members are there in the club now?

x =  64

### Step-by-step explanation:

x = b+g
b=g
b = 4/3 · (g-8)

b+g-x = 0
b-g = 0
3b-4g = -32

Pivot: Row 1 ↔ Row 3
3b-4g = -32
b-g = 0
b+g-x = 0

Row 2 - 1/3 · Row 1 → Row 2
3b-4g = -32
0.333g = 10.667
b+g-x = 0

Row 3 - 1/3 · Row 1 → Row 3
3b-4g = -32
0.333g = 10.667
2.333g-x = 10.667

Pivot: Row 2 ↔ Row 3
3b-4g = -32
2.333g-x = 10.667
0.333g = 10.667

Row 3 - 0.33333333/2.33333333 · Row 2 → Row 3
3b-4g = -32
2.333g-x = 10.667
0.143x = 9.143

x = 9.14285714/0.14285714 = 64
g = 10.66666667+x/2.33333333 = 10.66666667+64/2.33333333 = 32
b = -32+4g/3 = -32+4 · 32/3 = 32

b = 32
g = 32
x = 64

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