Ina family of 4 adults and some minors, the average consumptionof rice per head per month is 8.5 kg, while the average consumption for adults is 10 kg per head and for minorit is 5.5 kg per head. The numberof minors in the family is:

Options

A. 3
B. 5
C. 4
D. 2

Answer

To find the number of minors in the family, we can follow these steps:

### Step 1: Define Variables
Let the number of minors in the family be represented by \( x \).

### Step 2: Calculate Total Consumption for Adults
The average consumption of rice per adult is 10 kg. Since there are 4 adults, the total consumption for adults is:
\[ \text{Total consumption for adults} = 4 \times 10 = 40 \text{ kg} \]

### Step 3: Calculate Total Consumption for Minors
The average consumption of rice per minor is 5.5 kg. Therefore, the total consumption for minors is:
\[ \text{Total consumption for minors} = 5.5 \times x = 5.5x \text{ kg} \]

### Step 4: Calculate Total Consumption for the Family
The total number of people in the family is \( 4 + x \) (4 adults and \( x \) minors). The average consumption per head is given as 8.5 kg. Thus, the total consumption for the family can be expressed as:
\[ \text{Total consumption for family} = 8.5 \times (4 + x) \]

### Step 5: Set Up the Equation
Now we can set up the equation based on the total consumption:
\[ 40 + 5.5x = 8.5(4 + x) \]

### Step 6: Expand and Simplify the Equation
Expanding the right side:
\[ 40 + 5.5x = 34 + 8.5x \]

### Step 7: Rearrange the Equation
Now, rearranging the equation to isolate \( x \):
\[ 40 - 34 = 8.5x - 5.5x \]
\[ 6 = 3x \]

### Step 8: Solve for \( x \)
Dividing both sides by 3 gives:
\[ x = 2 \]

### Conclusion
The number of minors in the family is \( \boxed{2} \).

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