How many job applicants had applied if the ratio of selected to unselected was `19 : 17`. If 1,200 less had applied and 800 less selected, then the ratio of selected to unselected would have been `1 : 1`.

Options

A. 6000
B. 7200
C. 8400
D. 4800

Answer

To solve the problem step by step, we will use the information given about the ratios of selected and unselected job applicants.

### Step 1: Define the Variables
Let the number of selected applicants be \( 19x \) and the number of unselected applicants be \( 17x \).

### Step 2: Calculate Total Applicants
The total number of applicants can be expressed as:
\[ \text{Total Applicants} = \text{Selected} + \text{Unselected} = 19x + 17x = 36x \]

### Step 3: Set Up the New Scenario
According to the problem, if 1,200 less had applied and 800 less were selected, the new numbers would be:
- New Total Applicants = \( 36x - 1200 \)
- New Selected Applicants = \( 19x - 800 \)
- New Unselected Applicants = \( 17x \) (remains the same)

### Step 4: Establish the New Ratio
The new ratio of selected to unselected applicants is given as \( 1:1 \). Therefore, we can set up the equation:
\[ 19x - 800 = 17x \]

### Step 5: Solve the Equation
Rearranging the equation gives:
\[ 19x - 17x = 800 \]
\[ 2x = 800 \]
\[ x = 400 \]

### Step 6: Calculate Total Applicants
Now that we have the value of \( x \), we can find the total number of applicants:
\[ \text{Total Applicants} = 36x = 36 \times 400 = 14400 \]

### Final Answer
The total number of job applicants that had applied is **14,400**.

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