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.

Try another example


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







Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Do you have a system of equations and are looking for calculator system of linear equations?

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

Grade of the word problem:

Related math problems and questions: