Languages 7160

Out of 100 students, 30 studied German, 28 studied German, 42 learned French, eight studied German and German, 10 German and German, and 5 German and German. How many students have learned all three languages?

Correct answer:

p =  23

Step-by-step explanation:


100 = f+n+s+5+10+8-2p
42 = f+5+10-p
30 = n+5+8-p
28=s+8+10-p

100 = f+n+s+5+10+8-2·p
42 = f+5+10-p
30 = n+5+8-p
28=s+8+10-p

f+n-2p+s = 77
f-p = 27
n-p = 17
p-s = -10

Row 2 - Row 1 → Row 2
f+n-2p+s = 77
-n+p-s = -50
n-p = 17
p-s = -10

Row 3 + Row 2 → Row 3
f+n-2p+s = 77
-n+p-s = -50
-s = -33
p-s = -10

Pivot: Row 3 ↔ Row 4
f+n-2p+s = 77
-n+p-s = -50
p-s = -10
-s = -33


s = -33/-1 = 33
p = -10+s = -10+33 = 23
n = -50-p+s/-1 = -50-23+33/-1 = 40
f = 77-n+2p-s = 77-40+2 · 23-33 = 50

f = 50
n = 40
p = 23
s = 33

Our linear equations calculator calculates it.

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Grade of the word problem:

Related math problems and questions: