A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?

Options

A. 30
B. 20
C. 19
D. 18

Explanation

To solve the problem, we need to determine how many of the 60 tents were 2-person tents given that there are a total of 202 people camping.

### Step 1: Define Variables
Let:
- \( x \) = the number of 2-person tents
- \( y \) = the number of 4-person tents

### Step 2: Set Up Equations
From the information provided, we can form two equations:
1. The total number of tents:
\[ x + y = 60 \quad \text{(Equation 1)} \]
2. The total number of people:
\[ 2x + 4y = 202 \quad \text{(Equation 2)} \]

### Step 3: Solve for One Variable
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 60 - x \]

### Step 4: Substitute into the Second Equation
Now, substitute \( y \) in Equation 2:
\[ 2x + 4(60 - x) = 202 \]

### Step 5: Simplify the Equation
Distributing the 4:
\[ 2x + 240 - 4x = 202 \]
Combine like terms:
\[ -2x + 240 = 202 \]

### Step 6: Isolate the Variable
Subtract 240 from both sides:
\[ -2x = 202 - 240 \]
\[ -2x = -38 \]
Now, divide by -2:
\[ x = 19 \]

### Step 7: Find the Number of 4-Person Tents
Now that we have \( x \), we can find \( y \):
\[ y = 60 - x = 60 - 19 = 41 \]

### Conclusion
Thus, the number of 2-person tents is \( \boxed{19} \).

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