2186 are distributed among A,B and C. If money given to them is decreased by 26, 28 and 32 respectively, then they have money in the ratio of 9 : 13 : 8. What is the amount given to A?

Options

A. x 575
B. x 640
C. x 656
D. x 672

Answer

To solve the problem step by step, we will first set up the equations based on the information provided.

### Step 1: Define the amounts given to A, B, and C
Let the amounts given to A, B, and C be represented as follows:
- Amount given to A = \( 9k + 26 \)
- Amount given to B = \( 13k + 28 \)
- Amount given to C = \( 8k + 32 \)

### Step 2: Set up the equation based on the total amount distributed
According to the problem, the total amount distributed among A, B, and C is 2186. Therefore, we can write the equation:
\[ (9k + 26) + (13k + 28) + (8k + 32) = 2186 \]

### Step 3: Simplify the equation
Now, we will combine like terms:
\[ 9k + 13k + 8k + 26 + 28 + 32 = 2186 \]
This simplifies to:
\[ 30k + 86 = 2186 \]

### Step 4: Solve for \( k \)
Next, we will isolate \( k \) by first subtracting 86 from both sides:
\[ 30k = 2186 - 86 \]
\[ 30k = 2100 \]
Now, divide both sides by 30:
\[ k = \frac{2100}{30} = 70 \]

### Step 5: Calculate the amount given to A
Now that we have the value of \( k \), we can find the amount given to A:
\[ \text{Amount given to A} = 9k + 26 = 9(70) + 26 \]
Calculating this gives:
\[ = 630 + 26 = 656 \]

### Final Answer
The amount given to A is **656**.

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