A grid is made up of 13 rows of squares , each having 14 identical squares, Bolo comes and wants to draw some more square to the girl. So , he draw 3 additional rows and add 'S' additional squares in each row, including the ones he added himself . Which of the following expression correctly represents the increase in the total number of squares in the grid ?

Options

A. 11+5n
B. 42 + 16m
C. 60 + 12n
D. 224 + 16 n

Answer

To find the increase in the total number of squares in the grid after Bolo's additions, we can break down the problem step by step.

### Step 1: Calculate the initial number of squares
The grid initially has 13 rows, each containing 14 squares.

\[ \text{Initial number of squares} = 13 \text{ rows} \times 14 \text{ squares/row} = 182 \text{ squares} \]

### Step 2: Calculate the number of additional rows
Bolo adds 3 additional rows to the grid.

\[ \text{Additional rows} = 3 \]

### Step 3: Calculate the total number of rows after Bolo's addition
The total number of rows after adding the additional rows is:

\[ \text{Total rows} = 13 \text{ initial rows} + 3 \text{ additional rows} = 16 \text{ rows} \]

### Step 4: Calculate the total number of squares in the new grid
Each of the 16 rows still has 14 squares, so the total number of squares in the new grid is:

\[ \text{Total squares in new grid} = 16 \text{ rows} \times 14 \text{ squares/row} = 224 \text{ squares} \]

### Step 5: Calculate the increase in the number of squares due to additional rows
Bolo's addition of 3 rows means he has added:

\[ \text{Squares added by new rows} = 3 \text{ rows} \times 14 \text{ squares/row} = 42 \text{ squares} \]

### Step 6: Calculate the additional squares added in each row
Bolo adds 'S' additional squares in each of the 16 rows. Therefore, the total number of additional squares added is:

\[ \text{Additional squares} = 16 \text{ rows} \times S \text{ squares/row} = 16S \text{ squares} \]

### Step 7: Calculate the total increase in the number of squares
The total increase in the number of squares due to the additional rows and the additional squares is:

\[ \text{Total increase} = \text{Squares added by new rows} + \text{Additional squares} \]

Substituting the values we calculated:

\[ \text{Total increase} = 42 + 16S \]

### Final Expression
Thus, the expression that correctly represents the increase in the total number of squares in the grid is:

\[ \text{Increase in total squares} = 42 + 16S \]

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