A total of 57 sweets were distributed among 10 children such that each girl gets 6 sweets and each boy gets 5 sweets. The number of boys is :

Options

A. 6
B. 4
C. 3
D. 5

Answer

To solve the problem of distributing 57 sweets among 10 children, where each girl receives 6 sweets and each boy receives 5 sweets, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = number of boys
- \( y \) = number of girls

### Step 2: Set Up the Equations
From the problem, we know two things:
1. The total number of children is 10:
\[ x + y = 10 \]
2. The total number of sweets distributed is 57:
\[ 5x + 6y = 57 \]

### Step 3: Solve the First Equation for One Variable
We can express \( y \) in terms of \( x \) using the first equation:
\[ y = 10 - x \]

### Step 4: Substitute into the Second Equation
Now, substitute \( y \) in the second equation:
\[ 5x + 6(10 - x) = 57 \]

### Step 5: Simplify the Equation
Distributing the 6:
\[ 5x + 60 - 6x = 57 \]
Combine like terms:
\[ -1x + 60 = 57 \]

### Step 6: Solve for \( x \)
Subtract 60 from both sides:
\[ -1x = 57 - 60 \]
\[ -1x = -3 \]
Now, multiply both sides by -1:
\[ x = 3 \]

### Step 7: Find the Number of Girls
Using the value of \( x \) to find \( y \):
\[ y = 10 - x = 10 - 3 = 7 \]

### Conclusion
The number of boys is \( x = 3 \).