Some questions are solved on the basis of a certain system. Identify that operation and find out the correct answer from the four responses given.
a = 14(290)15 b= 16 (330) 17 c=18(?)19

Options

A. 300
B. 270
C. 170
D. 370

Explanation

To solve the problem, we will identify the operation used in the given equations and apply it to find the missing value in the third equation.

### Given Equations:
1. \( a = 14(290)15 \)
2. \( b = 16(330)17 \)
3. \( c = 18(?)19 \)

### Step-by-Step Solution:

**Step 1: Analyze the first equation \( a = 14(290)15 \)**
- Calculate the sum of the first and last numbers:
\[ 14 + 15 = 29 \]
- Multiply the sum by 10:
\[ 29 \times 10 = 290 \]
- This confirms that the operation holds for the first equation.

**Step 2: Analyze the second equation \( b = 16(330)17 \)**
- Calculate the sum of the first and last numbers:
\[ 16 + 17 = 33 \]
- Multiply the sum by 10:
\[ 33 \times 10 = 330 \]
- This confirms that the operation holds for the second equation.

**Step 3: Apply the same operation to the third equation \( c = 18(?)19 \)**
- Calculate the sum of the first and last numbers:
\[ 18 + 19 = 37 \]
- Multiply the sum by 10:
\[ 37 \times 10 = 370 \]

### Conclusion:
Thus, the missing value in the third equation is \( 370 \).

### Final Answer:
The correct answer is \( 370 \).

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