Theatre performances

A total of 15,744 CZK was collected as admission for three theatre performances. The revenue from the second performance was 20% higher than the revenue from the first performance and the revenue from the third performance was 10% lower than the revenue from the second performance. How many tickets priced at 64 CZK were sold for each performance?

Correct answer:

a =  75
b =  90
c =  81

Step-by-step explanation:


a+b+c = 15744/64
b = a + 20/100 a
c = b - 10/100b

a+b+c = 15744/64
b = a + 20/100·a
c = b - 10/100·b

64a+64b+64c = 15744
120a-100b = 0
90b-100c = 0

Pivot: Row 1 ↔ Row 2
120a-100b = 0
64a+64b+64c = 15744
90b-100c = 0

Row 2 - 64/120 · Row 1 → Row 2
120a-100b = 0
117.333b+64c = 15744
90b-100c = 0

Row 3 - 90/117.33333333 · Row 2 → Row 3
120a-100b = 0
117.333b+64c = 15744
-149.091c = -12076.364


c = -12076.36363636/-149.09090909 = 81
b = 15744-64c/117.33333333 = 15744-64 · 81/117.33333333 = 90
a = 0+100b/120 = 0+100 · 90/120 = 75

a = 75
b = 90
c = 81

Our linear equations calculator calculates it.



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