Question 86552: Humans have about 1,400,000 hairs on their head and lose an average of 75 hairs each day. If a person's body were to never replace a hair, approximately how many years would it take for a person to have 1000 hairs left on their head? (Assume that a person can live significantly longer than the average life span.)
Found 2 solutions by Nate, bucky:
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! 1,400,000 - 75x = y
where x is the amount of days and y is the amount of hairs left
1,400,000 - 75x = 1,000
1,399,000 = 75x
18,653 1/3 days / 356 = about 52 2/5 years
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! On the average human head there are 1,400,000 hairs. If you take away 75 hairs every day
in N days you will have taken away 75*N hairs. For example, in 10 days you would have
taken away 75*10 or 750 hairs.
.
After N days the number of hairs you will have left (call it H) is 1,400,000 less the
75*N hairs that have been lost. In equation form this is:
.
H = 1,400,000 - 75*N
.
The problem tells you that H is to be 1,000. Substituting this into the equation results in:
.
1,000 = 1,400,000 - 75*N
.
Let's get the term containing N over to the left side of the equation. We can do that by
adding 75*N to both sides. This addition results in:
.
75*N + 1,000 = 1,400,000
.
Next, let's get the 1,000 on the left side moved over to the right side. Do this by subtracting
1,000 from both sides. This subtraction of 1,000 from both sides reduces the equation to:
.
75*N = 1,399,000
.
Now we can solve for N by dividing both sides of the equation by 75 (the multiplier
of N) to get:
.
N = 1,399,000/75 = 18,653
.
The actual answer is 18,653.3333 but I've rounded it off to a whole number of days.
.
Note that if you take 365 as the number of days in a year, this number of days is equal to:
.
18,653/365 = 51 years
.
Actually, it's about 51.10 years, but I've rounded this off to an even number of years also.
.
And the 1,000 hairs that are left will be gone (at the rate of 75 hairs lost per day) in:
.
N = 1,000/75 = 13.3 days.
.
So two weeks after you're down to 1,000 hairs you would be bald as a basketball.
.
Hope this helps you to understand the problem.
|
|
|
