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# Ancient Sickness problem ?

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According to an ancient belief, when a friend visits a sick person, $$\frac{1}{60}$$ of his or her illness is taken away. How many friends need to visit to take away at least 99% of a person's illness?

A. 375

B. 180

C. 275

D. 125

E. 55

Please explain, I am confused on this problem

Feb 16, 2019
edited by CalculatorUser  Feb 16, 2019

### 3+0 Answers

#1
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If 1/60 is taken away after a visit .....then 59/60  must remain after a visit

So.....we want to find out how many visits are required to have   1%  =  1/100 left

So.....we want to solve this

(59/60)^N  =   1/100         where N is the number of required friends

Take the log of both sides

log (59/60)^N  =  log (1/100)      and by a log property, we can write

N * log (59/60) = log (1/100)     divide both sides by log(59/60)

N =    log(1/100) / log (59/60)   ≈  274.001 friends

We'll call  275  good      .....!!!

Feb 16, 2019
edited by CPhill  Feb 16, 2019
#2
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Thanks CPhill! I understand now!

Feb 16, 2019
#3
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OK, CU.....glad to  help....

CPhill  Feb 16, 2019