Divide 37 into two parts so that 5 times one part and 11 times the other are together 227. The parts are

Options

A. 15, 22
B. 20, 17
C. 25,12
D. 30, 7

Answer

To solve the problem of dividing 37 into two parts such that 5 times one part and 11 times the other part sum up to 227, we can follow these steps:

### Step 1: Define the Parts
Let the first part be \( x \) and the second part be \( y \). According to the problem, we have:
\[ x + y = 37 \quad \text{(Equation 1)} \]

### Step 2: Set Up the Second Equation
The problem states that 5 times the first part and 11 times the second part equal 227. This gives us the second equation:
\[ 5x + 11y = 227 \quad \text{(Equation 2)} \]

### Step 3: Solve for One Variable
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 37 - x \]

### Step 4: Substitute into the Second Equation
Now, substitute \( y \) in Equation 2:
\[ 5x + 11(37 - x) = 227 \]

### Step 5: Simplify the Equation
Distributing the 11:
\[ 5x + 407 - 11x = 227 \]
Combine like terms:
\[ -6x + 407 = 227 \]

### Step 6: Isolate \( x \)
Subtract 407 from both sides:
\[ -6x = 227 - 407 \]
\[ -6x = -180 \]
Divide by -6:
\[ x = 30 \]

### Step 7: Find \( y \)
Now, substitute \( x \) back into Equation 1 to find \( y \):
\[ y = 37 - 30 = 7 \]

### Conclusion
The two parts are:
\[ \text{First part } (x) = 30, \quad \text{Second part } (y) = 7 \]

### Final Answer
The parts are \( 30 \) and \( 7 \).

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