Problem Solving

coolhabhi wrote:The average age of 40 women decreases by 1/8th of a year when one of them whose age is 50 years is replaced by a new woman. Find the age of the new woman.
a)36 years
b)42 years
c)45 years
d)43 years

We're told that the new average age is 1/8 years less than the original average age.
Let's start with a "word equation"
(original average age) - (new average age) = 1/8
So, (original sum of 40 women)/40 - (new sum of 40 women)/40 = 1/8
Multiply both side by 40 to get: (original sum of 40 women) - (new sum of 40 women) = 5

IMPORTANT: Notice that the two sums both have the same 39 ages. All that changes is that we replace the 50-year old, with a woman who is x years old.

In other words, (sum of 39 ages + 50) - (sum of 39 ages + x) = 5
Simplify to get: 50 - x = 5
x = [spoiler]45 = C[/spoiler]

Cheers,
Brent

coolhabhi wrote: ↑

Sat Oct 19, 2013 3:02 am

The average age of 40 women decreases by 1/8th of a year when one of them whose age is 50 years is replaced by a new woman. Find the age of the new woman.
a)36 years
b)42 years
c)45 years
d)43 years

OAC

Got the answer but need a simple and quick solution.

We can let a = the average age of the original 40 women and x = the age of the new woman. We can create the equation:

(40a - 50 + x) / 40 = a - 1/8

40a - 50 + x = 40(a - 1/8)

40a - 50 + x = 40a - 5

x = 45

Answer: C