Salary in enterprise

The average salary in the company is 27,000 CZK. 30% of workers have the lowest average income of 19,000 CZK. The wages in this group increased by 2%. How much did this increase the average wage across the company?

Correct answer:

p =  0.4222 %

Step-by-step explanation:


a=19000
0.3·a + 0.7·b = 27000
c = 0.3·a·1.02 + 0.7·b
p = 100·(c/27000-1)

a = 19000
0.3a+0.7b = 27000
0.306a+0.7b-c = 0
100c-27000p = 2700000

Row 2 - 0.29999999999927 · Row 1 → Row 2
a = 19000
0.7b = 21300
0.306a+0.7b-c = 0
100c-27000p = 2700000

Row 3 - 0.306 · Row 1 → Row 3
a = 19000
0.7b = 21300
0.7b-c = -5814
100c-27000p = 2700000

Row 3 - 0.7/0.7 · Row 2 → Row 3
a = 19000
0.7b = 21300
-c = -27114
100c-27000p = 2700000

Pivot: Row 3 ↔ Row 4
a = 19000
0.7b = 21300
100c-27000p = 2700000
-c = -27114

Row 4 - -1/100 · Row 3 → Row 4
a = 19000
0.7b = 21300
100c-27000p = 2700000
-270p = -114


p = -113.99999999/-270 = 0.42222222
c = 2700000+27000p/100 = 2700000+27000 · 0.42222222/100 = 27113.99999999
b = 21300.00000001/0.7 = 30428.57142856
a = 19000/1 = 19000

a = 19000
b = 213000/7 ≈ 30428.571429
c = 27114
p = 19/45 ≈ 0.422222

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