Fourth-week 17783

They earned CZK 113,400 in the shop in four weeks. The first and fourth-week sales were the same, the second week 10% higher than the first week and the third week 5% lower than the first week. How much did they earn each week?

Correct answer:

a = 28000
b = 30800
c = 26600
d = 28000

Step-by-step explanation:

113400 = a+b+c+d
a=d
b = a + 1/10a
c = a - 5/100a

113400 = a+b+c+d
a=d
b = a + 1/10·a
c = a - 5/100·a

a+b+c+d = 113400
a-d = 0
11a-10b = 0
95a-100c = 0

Pivot: Row 1 ↔ Row 4
95a-100c = 0
a-d = 0
11a-10b = 0
a+b+c+d = 113400

Row 2 - 1/95 · Row 1 → Row 2
95a-100c = 0
1.0526c-d = 0
11a-10b = 0
a+b+c+d = 113400

Row 3 - 11/95 · Row 1 → Row 3
95a-100c = 0
1.0526c-d = 0
-10b+11.5789c = 0
a+b+c+d = 113400

Row 4 - 1/95 · Row 1 → Row 4
95a-100c = 0
1.0526c-d = 0
-10b+11.5789c = 0
b+2.0526c+d = 113400

Pivot: Row 2 ↔ Row 3
95a-100c = 0
-10b+11.5789c = 0
1.0526c-d = 0
b+2.0526c+d = 113400

Row 4 - 1/-10 · Row 2 → Row 4
95a-100c = 0
-10b+11.5789c = 0
1.0526c-d = 0
3.2105c+d = 113400

Pivot: Row 3 ↔ Row 4
95a-100c = 0
-10b+11.5789c = 0
3.2105c+d = 113400
1.0526c-d = 0

Row 4 - 1.05263158/3.21052632 · Row 3 → Row 4
95a-100c = 0
-10b+11.5789c = 0
3.2105c+d = 113400
-1.3279d = -37180.3279

d = -37180.32786885/-1.32786885 = 28000
c = 113400-d/3.21052632 = 113400-28000/3.21052632 = 26600
b = 0-11.578947368421c/-10 = 0-11.57894737 · 26600/-10 = 30800
a = 0+100c/95 = 0+100 · 26600/95 = 28000

a = 28000
b = 30800
c = 26600
d = 28000

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