Simplify

$\frac{92736}{(274+830)\text{of }\frac{7}{4}}+513$

The correct answer is 561.

To simplify the given expression, we follow the order of operations (BODMAS/PEMDAS rule):

$\frac{92736}{(274+830)\text{ of }\frac{7}{4}}+513$

Step 1: Solve the expression inside the parentheses
First, perform the addition in the denominator:

$274+830=1104$

Step 2: Solve the "of" operator (which signifies multiplication)
Now, calculate the product of the result and 7/4:

$1104\text{ of }\frac{7}{4}=1104\times \frac{7}{4}$

Dividing 1104 by 4 gives 276:

$276\times 7=1932$

Now our original expression becomes:

$\frac{92736}{1932}+513$

Step 3: Perform division
Divide 92736 by 1932:

$\frac{92736}{1932}=48$

Step 4: Perform the final addition
Add the results to find the final value:

$48+513=561$