Originally 2822

There were plums in the basket. They doubled their number and then took 8 plums. They doubled the number of plums left in the basket again and took 8 plums. They doubled the number once more and took 8 plums. Then, there was no plum left in the basket. How many plums were originally in the basket?

Correct answer:

x =  7

Step-by-step explanation:


a=2x-8
b = 2a-8
c = 2b-8
c = 0

a=2·x-8
b = 2·a-8
c = 2·b-8
c = 0

a-2x = -8
2a-b = 8
2b-c = 8
c = 0

Pivot: Row 1 ↔ Row 2
2a-b = 8
a-2x = -8
2b-c = 8
c = 0

Row 2 - 1/2 · Row 1 → Row 2
2a-b = 8
0.5b-2x = -12
2b-c = 8
c = 0

Pivot: Row 2 ↔ Row 3
2a-b = 8
2b-c = 8
0.5b-2x = -12
c = 0

Row 3 - 0.5/2 · Row 2 → Row 3
2a-b = 8
2b-c = 8
0.25c-2x = -14
c = 0

Pivot: Row 3 ↔ Row 4
2a-b = 8
2b-c = 8
c = 0
0.25c-2x = -14

Row 4 - 0.25 · Row 3 → Row 4
2a-b = 8
2b-c = 8
c = 0
-2x = -14


x = -14/-2 = 7
c = 0/1 = 0
b = 8+c/2 = 8/2 = 4
a = 8+b/2 = 8+4/2 = 6

a = 6
b = 4
c = 0
x = 7

Our linear equations calculator calculates it.



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