Pupils at cinema

Alena bought movie tickets for two groups of pupils. The first group purchased seven tickets for 1st and five for 2nd place, and she paid 62Kč. The second group bought 11 tickets for 1st and four for 2nd place and paid 82Kč. How much was the ticket for 1st and 2nd place?

Correct answer:

a =  6
b =  4

Step-by-step explanation:

7a+5b=62
11a+4b=82

7·a+5·b=62
11·a+4·b=82

7a+5b = 62
11a+4b = 82

Pivot: Row 1 ↔ Row 2
11a+4b = 82
7a+5b = 62

Row 2 - 7/11 · Row 1 → Row 2
11a+4b = 82
2.45b = 9.82


b = 9.81818182/2.45454545 = 4
a = 82-4b/11 = 82-4 · 4/11 = 6

a = 6
b = 4

Our linear equations calculator calculates it.

Try another example