Question 4839
I am assuming you mean 25,000 in 1955 rather than 1995...

Let T = number of people in Tampa in 1955
Let A = number of people in Anchorage in 1955

Let .10A = The number of people Anchorage increased by
Let .09T = The number of people Tampa increased by

We know that the 1955 population from Tampa and Anchorage = 25000 people, so:
T+A=25000, or by subtracting A from both sides we can get:
T=25000-A

And because the population increase was 2380 people, we can say:
.10A+.09T=2380

Us substitution:
.10A+.09T=2380
.10A+.09(25000-A)=2380

Clear parentheses, and combine like terms:
.10A+2250-.09A=2380
.01A+2250=2380
.01A=130
A=13000

Use one of your equations to get the T result:
T+A=25000
T+13000=25000
T=12000

Check your results with the other formula:
.10(13000)+.09(12000)=2380
1300+1080=2380

This is a true statement, so the solution is:
Anchorage 1955 population = 13000
Tampa 1955 population = 12000