Question

A census showed that from 1990 to 2000, a country’s population increased by 25.3%. The country reported its population in 2000 to be 15,264,465. What was the country’s population in 1990?

Answer 1

Answer:

12,182,334

Step-by-step explanation:

If some quantity q increases by r%, then the increment will be $\frac{qr}{100}$. The new quantity Q (increased) will be

$Q=q+\frac{qr}{100}=q(1+\frac{r}{100})$

If we know the final quantity, we can know the original q as

$\displaystyle q=\frac{Q}{1+\frac{r}{100} }$

The census showed the rate of increase of the population was r=25.3% and the final population in 2000 was Q=15,264,465. So we can know the population back in 1990 was

$\displaystyle q=\frac{15,264,465}{1+\frac{25.3}{100}}\approx 12,182,334$