A student a pages day for d day and then reads b page per day for 2d days . In terms of a,b,and d , how many pages did the student read ?

Options

A. `ad +2b`
B. `ad+2bd`
C. `2ad +2bd`
D. `2abd`

Answer

To find out how many pages the student read in total, we can break down the problem step by step.

### Step 1: Calculate pages read in the first period
The student reads **a** pages per day for **d** days. To find the total pages read during this period, we multiply the number of pages read per day by the number of days:

\[ \text{Pages read in first period} = a \times d = a \cdot d \]

### Step 2: Calculate pages read in the second period
Next, the student reads **b** pages per day for **2d** days. Similarly, we calculate the total pages read during this period:

\[ \text{Pages read in second period} = b \times (2d) = b \cdot 2d = 2b \cdot d \]

### Step 3: Calculate total pages read
Now, we add the pages read in both periods to find the total number of pages read by the student:

\[ \text{Total pages read} = \text{Pages read in first period} + \text{Pages read in second period} \]

Substituting the values from the previous steps:

\[ \text{Total pages read} = (a \cdot d) + (2b \cdot d) \]

### Step 4: Factor out common terms
We can factor out **d** from the total pages read:

\[ \text{Total pages read} = d(a + 2b) \]

### Final Answer
So, the total number of pages read by the student in terms of **a**, **b**, and **d** is:

\[ \text{Total pages read} = a \cdot d + 2b \cdot d \]