The business

The business earned CZK 98,400 in the shop in three weeks. In the second week, sales were 20% higher than the first week. The third week was 10% lower than the second week. How much did the business earn each week?

Correct answer:

a =  30000
b =  36000
c =  32400

Step-by-step explanation:


a+b+c=98400
b = a + 20/100 a
c = b - 10/100 b

a+b+c=98400
b = a + 20/100·a
c = b - 10/100·b

a+b+c = 98400
120a-100b = 0
90b-100c = 0

Pivot: Row 1 ↔ Row 2
120a-100b = 0
a+b+c = 98400
90b-100c = 0

Row 2 - 1/120 · Row 1 → Row 2
120a-100b = 0
1.833b+c = 98400
90b-100c = 0

Pivot: Row 2 ↔ Row 3
120a-100b = 0
90b-100c = 0
1.833b+c = 98400

Row 3 - 1.83333333/90 · Row 2 → Row 3
120a-100b = 0
90b-100c = 0
3.037c = 98400


c = 98400/3.03703704 = 32400
b = 0+100c/90 = 0+100 · 32400/90 = 36000
a = 0+100b/120 = 0+100 · 36000/120 = 30000

a = 30000
b = 36000
c = 32400

Our linear equations calculator calculates it.



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