Determine the approximate value that should replace the question mark (?) in the following expression. (Note: You are expected to estimate rather than compute the precise value).

$59.77\%\text{of}880+79.9\%\text{of}591=?$

The correct option is 1000.

To find the approximate value of the expression, we round each number to its nearest convenient value for mental calculation:

1. Round $59.77\%$ to approximately $60\%$.

2. Keep $880$ as it is, or round $59.77\%\text{of}880$ to $60\%\text{of}880$.

3. Round $79.9\%$ to approximately $80\%$.

4. Round $591$ to approximately $590$.

Now, calculate each term step-by-step:

First term:

$60\%\text{of}880=\frac{60}{100}\times 880=6\times 88=528$

Second term:

$80\%\text{of}590=\frac{80}{100}\times 590=8\times 59=472$

Combine both terms:

$?\approx 528+472=1000$

Thus, the approximate value that replaces the question mark is 1000.