# Question dba1a

Feb 21, 2017

The population 2 years hence was 2000 people.

#### Explanation:

For each year, the end population is 90% of the starting population (100%). That means that:
1620=90%
and
x=100%#

So, to know the population from a year ago, we have to set up the following equality:
$\frac{1620}{x} = \frac{90}{100}$

Now, with a little algebra we do the following steps to single out $x$"

1) multiply each side by $x$
$\cancel{x} \cdot \frac{1620}{\cancel{x}} = \frac{90}{100} \cdot x$

2) multiply each side by 100
$100 \cdot 1620 = x \cdot \frac{90}{\cancel{100}} \cdot \cancel{100}$

3) multiply each side by $\frac{1}{90}$
$\frac{1}{90} \cdot 100 \cdot 1620 = x \cdot \cancel{90} \cdot \frac{1}{\cancel{90}}$

Leaving us with:
$x = \frac{100 \cdot 1620}{90}$ which is equal to $1800$

Now if we do the same process with 1800 to start with, we get the final equation:
$x = \frac{100 \cdot 1800}{90}$ which is equal to $2000$