If seven times of certain number 'a' is ten more than twice the number, then equation derived for this statement can be written as-

Options

A. 2a = 7a + 10
B. 2a = 7a - 10
C. 7a = 2a/10
D. 2a = 7a + 20

Answer

To solve the problem step by step, we need to translate the verbal statement into a mathematical equation.

### Step 1: Identify the components of the statement
The statement says "seven times a certain number 'a'." This can be expressed mathematically as:
\[ 7a \]

### Step 2: Understand the second part of the statement
The statement continues with "is ten more than twice the number." The phrase "twice the number" refers to:
\[ 2a \]
So, "ten more than twice the number" can be expressed as:
\[ 2a + 10 \]

### Step 3: Set up the equation
Now, we can combine both parts of the statement into an equation. The first part (seven times the number) is equal to the second part (ten more than twice the number):
\[ 7a = 2a + 10 \]

### Step 4: Rearrange the equation
To isolate 'a', we can rearrange the equation. We can subtract \(2a\) from both sides:
\[ 7a - 2a = 10 \]
This simplifies to:
\[ 5a = 10 \]

### Step 5: Solve for 'a'
Now, divide both sides by 5 to find the value of 'a':
\[ a = \frac{10}{5} \]
So, we get:
\[ a = 2 \]

### Final Equation
The equation derived from the statement is:
\[ 7a = 2a + 10 \]