English-German 6443

Two foreign languages ​​are compulsory from the fourth grade. Only a tenth of the class did not choose English, and a fifth did not take German. Fifteen children learn French this way. Calculate how many pupils chose the English-German combination.

Correct answer:

b =  35

Step-by-step explanation:


a+b+c = n
c = n/10
a = n/5
a+c=15

a+b+c-n = 0
10c-n = 0
5a-n = 0
a+c = 15

Pivot: Row 1 ↔ Row 3
5a-n = 0
10c-n = 0
a+b+c-n = 0
a+c = 15

Row 3 - 1/5 · Row 1 → Row 3
5a-n = 0
10c-n = 0
b+c-0.8n = 0
a+c = 15

Row 4 - 1/5 · Row 1 → Row 4
5a-n = 0
10c-n = 0
b+c-0.8n = 0
c+0.2n = 15

Pivot: Row 2 ↔ Row 3
5a-n = 0
b+c-0.8n = 0
10c-n = 0
c+0.2n = 15

Row 4 - 1/10 · Row 3 → Row 4
5a-n = 0
b+c-0.8n = 0
10c-n = 0
0.3n = 15


n = 15/0.3 = 50
c = 0+n/10 = 0+50/10 = 5
b = 0-c+0.8n = 0-5+0.8 · 50 = 35
a = 0+n/5 = 0+50/5 = 10

a = 10
b = 35
c = 5
n = 50

Our linear equations calculator calculates it.



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