# Difference between revisions of "1998 AJHSME Problems/Problem 15"

## Don't Crowd the Isles

Problems 15, 16, and 17 all refer to the following:

In the very center of the Irenic Sea lie the beautiful Nisos Isles. In 1998 the number of people on these islands is only 200, but the population triples every 25 years. Queen Irene has decreed that there must be at least 1.5 square miles for every person living in the Isles. The total area of the Nisos Isles is 24,900 square miles.

### Problem 15

Estimate the population of Nisos in the year 2050. $\text{(A)}\ 600 \qquad \text{(B)}\ 800 \qquad \text{(C)}\ 1000 \qquad \text{(D)}\ 2000 \qquad \text{(E)}\ 3000$

## Solution

The population triples every $25$ years from $200$, and there are $50$ years between $2000$ and $2050$, so we will have $200\times3=600\times3=1800$.

This is an underestimate, since there are actually $2$ more years for the island's population to grow.

Therefore, $1800$ can be rounded to $2000=\boxed{D}$

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 