Language 6588

Two hundred fifty-five students of a certain high school know one other language in addition to English. Twenty-three more pupils mastered the German language than the Russian language. The French language is mastered by 37 fewer pupils than the German language. How many pupils know the German language?

Correct answer:

n =  105

Step-by-step explanation:


255 = n+r+f
n = 23+r
f = n-37

f+n+r = 255
n-r = 23
f-n = -37

Row 3 - Row 1 → Row 3
f+n+r = 255
n-r = 23
-2n-r = -292

Pivot: Row 2 ↔ Row 3
f+n+r = 255
-2n-r = -292
n-r = 23

Row 3 - 1/-2 · Row 2 → Row 3
f+n+r = 255
-2n-r = -292
-1.5r = -123


r = -123/-1.5 = 82
n = -292+r/-2 = -292+82/-2 = 105
f = 255-n-r = 255-105-82 = 68

f = 68
n = 105
r = 82

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