The population of a town increases by 20% in each year starting 2010. If the total population of the two in 2013 is 77940, what was the population of the town is 2010?

Options

A. 60000
B. 45000
C. 40000
D. 35000

Answer

To find the population of the town in 2010 based on the given information, we will follow these steps:

### Step 1: Define the initial population
Let the population of the town in 2010 be \( x \).

### Step 2: Calculate the population for subsequent years
The population increases by 20% each year. We can express the population for each year as follows:

- **2011**:
\[ \text{Population} = x + 0.2x = 1.2x \]

- **2012**:
\[ \text{Population} = 1.2x + 0.2(1.2x) = 1.2x + 0.24x = 1.44x \]

- **2013**:
\[ \text{Population} = 1.44x + 0.2(1.44x) = 1.44x + 0.288x = 1.728x \]

### Step 3: Set up the equation
According to the problem, the total population in 2013 is 77940. Therefore, we can set up the equation:
\[ 1.728x = 77940 \]

### Step 4: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 1.728:
\[ x = \frac{77940}{1.728} \]

### Step 5: Calculate the value
Now, we perform the division:
\[ x \approx 45000 \]

### Conclusion
The population of the town in 2010 was approximately **45000**.

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