Two consecutive positive integers are multiplied. The product when rounded to the nearest hundred is 202100. Find the sum of the two positive integers. Answer ...

1. Set up an equation to estimate the value of the integers

Let the two consecutive positive integers be $n$ and $n+1$.
$n(n+1) \approx 202100$
$n^2 \approx 202100$
$n \approx \sqrt{202100} \approx 449.55$

2. Test integer values near the estimate to find the exact integers

Test $n = 449$:
$449 \times 450 = 202050$
When 202050 is rounded to the nearest hundred, it is 202100.
Thus, the two integers are 449 and 450.

3. Calculate the sum of the two integers

Sum $= 449 + 450 = 899$