One-quarter 5440

They delivered goods to four stores. First, they collected one-third of the shipment, second only two-thirds of what happened in the first. In the third, one-quarter of the rest, and the fourth, the remaining 240 kg. How much did they make at each store?

Correct answer:

a =  240
b =  160
c =  80
d =  240
s =  720

Step-by-step explanation:


a+b+c+d=s
d = 240
a = s/3
b = 2/3 · a
c = (s-a-b)/4

a+b+c+d-s = 0
d = 240
3a-s = 0
2a-3b = 0
a+b+4c-s = 0

Pivot: Row 1 ↔ Row 3
3a-s = 0
d = 240
a+b+c+d-s = 0
2a-3b = 0
a+b+4c-s = 0

Row 3 - 1/3 · Row 1 → Row 3
3a-s = 0
d = 240
b+c+d-0.66667s = 0
2a-3b = 0
a+b+4c-s = 0

Row 4 - 2/3 · Row 1 → Row 4
3a-s = 0
d = 240
b+c+d-0.66667s = 0
-3b+0.66667s = 0
a+b+4c-s = 0

Row 5 - 1/3 · Row 1 → Row 5
3a-s = 0
d = 240
b+c+d-0.66667s = 0
-3b+0.66667s = 0
b+4c-0.66667s = 0

Pivot: Row 2 ↔ Row 4
3a-s = 0
-3b+0.66667s = 0
b+c+d-0.66667s = 0
d = 240
b+4c-0.66667s = 0

Row 3 - 1/-3 · Row 2 → Row 3
3a-s = 0
-3b+0.66667s = 0
c+d-0.44444s = 0
d = 240
b+4c-0.66667s = 0

Row 5 - 1/-3 · Row 2 → Row 5
3a-s = 0
-3b+0.66667s = 0
c+d-0.44444s = 0
d = 240
4c-0.44444s = 0

Pivot: Row 3 ↔ Row 5
3a-s = 0
-3b+0.66667s = 0
4c-0.44444s = 0
d = 240
c+d-0.44444s = 0

Row 5 - 1/4 · Row 3 → Row 5
3a-s = 0
-3b+0.66667s = 0
4c-0.44444s = 0
d = 240
d-0.33333s = 0

Row 5 - Row 4 → Row 5
3a-s = 0
-3b+0.66667s = 0
4c-0.44444s = 0
d = 240
-0.33333s = -240


s = -240/-0.33333333 = 720
d = 240/1 = 240
c = 0+0.44444444444444s/4 = 0+0.44444444 · 720/4 = 80
b = 0-0.66666666666667s/-3 = 0-0.66666667 · 720/-3 = 160
a = 0+s/3 = 0+720/3 = 240

a = 240
b = 160
c = 80
d = 240
s = 720

Our linear equations calculator calculates it.



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