4. If there are $$ 4 x $$ identical schools in a region and each school has $$ 3 y $$ class- rooms each with $$ 7 x $$ desks, how many desks are there in the region? A. $$ 11 x+3 y $$ B. $$ 28 x+3 y $$ C. $$ 84 x y^{2} $$ D. $$ 84 x^{2} y $$ E. $$ 11 x(3 y) $$

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To find the total number of desks in the region, we can follow these steps:

1. **Identify the number of schools**: There are $$ 4x $$ identical schools.
2. **Identify the number of classrooms per school**: Each school has $$ 3y $$ classrooms.
3. **Identify the number of desks per classroom**: Each classroom has $$ 7x $$ desks.

Now, we can calculate the total number of desks in the region using the formula:

$$
\text{Total Desks} = (\text{Number of Schools}) \times (\text{Classrooms per School}) \times (\text{Desks per Classroom})
$$

Substituting the known values:

$$
\text{Total Desks} = (4x) \times (3y) \times (7x)
$$

Now, let's perform the multiplication step by step:

1. First, multiply the number of schools by the number of classrooms per school:
   $$
   4x \times 3y = 12xy
   $$

2. Next, multiply the result by the number of desks per classroom:
   $$
   12xy \times 7x = 84x^2y
   $$

Thus, the total number of desks in the region is:

$$
\text{Total Desks} = 84x^2y
$$

Now, let's check the answer choices:

A. $$ 11x + 3y $$  
B. $$ 28x + 3y $$  
C. $$ 84xy^2 $$  
D. $$ 84x^2y $$  
E. $$ 11x(3y) $$

The correct answer is:

**D. $$ 84x^2y $$**.
The total number of desks in the region is $$ 84x^2y $$, so the correct answer is D.

4. If there are \( 4 x \) identical schools in a region and each school has \( 3 y \) class- rooms each with \( 7 x \) desks, how many desks are there in the region? A. \( 11 x+3 y \) B. \( 28 x+3 y \) C. \( 84 x y^{2} \) D. \( 84 x^{2} y \) E. \( 11 x(3 y) \)

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