Two-thirds 2786

Two-thirds of girls and half of boys learn Spanish in the classroom. There are twice as many boys in the class as there are girls. What part of the class is learning Spanish?

Result

s = 5/9 Wrong answer

Step-by-step explanation:


m+f = 1
m = 2f
s = 2/3 f + 1/2 m

m+f = 1
m = 2·f
s = 2/3·f + 1/2·m

f+m = 1
2f-m = 0
4f+3m-6s = 0

Pivot: Row 1 ↔ Row 3
4f+3m-6s = 0
2f-m = 0
f+m = 1

Row 2 - 2/4 · Row 1 → Row 2
4f+3m-6s = 0
-2.5m+3s = 0
f+m = 1

Row 3 - 1/4 · Row 1 → Row 3
4f+3m-6s = 0
-2.5m+3s = 0
0.25m+1.5s = 1

Row 3 - 0.25/-2.5 · Row 2 → Row 3
4f+3m-6s = 0
-2.5m+3s = 0
1.8s = 1


s = 1/1.8 = 0.55555556
m = 0-3s/-2.5 = 0-3 · 0.55555556/-2.5 = 0.66666667
f = 0-3m+6s/4 = 0-3 · 0.66666667+6 · 0.55555556/4 = 0.33333333

f = 1/3 ≈ 0.333333
m = 2/3 ≈ 0.666667
s = 5/9 ≈ 0.555556

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