Asked by Anonymous
A tank contains a certain amount of water. Each month half of the water in the tank evaporates and an extra liter of water is added. After 5 months, after the litres of water is added, there were 4 litres of water in the tank. How many litres were in the tank originally?
Answers
Answered by
Steve
If there were x liters to start, then we have the following table:
month water at end of month
0 x
1 x/2 + 1
2 (x/2 + 1)/2 + 1 = x/4 + 3/2
3 (x/4 + 3/2)/2 + 1 = x/8 + 7/4
...
n x/2^n + (2*2^n-2)/2^n = (x + 2*2^n-2)/2^n
So, at the end of the 5th month there were
(x+62)/32 = 4
x = 66
check:
0 66
1 34
2 18
3 10
4 6
5 4
month water at end of month
0 x
1 x/2 + 1
2 (x/2 + 1)/2 + 1 = x/4 + 3/2
3 (x/4 + 3/2)/2 + 1 = x/8 + 7/4
...
n x/2^n + (2*2^n-2)/2^n = (x + 2*2^n-2)/2^n
So, at the end of the 5th month there were
(x+62)/32 = 4
x = 66
check:
0 66
1 34
2 18
3 10
4 6
5 4
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