Each boy in a class has 11 pockets and each girl in the class has 13 pockets

Each boy in a class has 11 pockets and each girl in the class has 13 pockets. How many boys and how many girls are in this class if all 21 students have a total of 251 pockets?

The correct answer and explanation is :

Let’s solve this problem step by step.

We know the following:

1. Each boy has 11 pockets.
2. Each girl has 13 pockets.
3. There are 21 students in total, consisting of boys and girls.
4. The total number of pockets for all students is 251.

Step 1: Set up variables

Let:

• $b$ represent the number of boys in the class.
• $g$ represent the number of girls in the class.

We are given:

• $b + g = 21$ (the total number of students).
• The total number of pockets is $11b + 13g = 251$ (since each boy has 11 pockets and each girl has 13 pockets).

Step 2: Solve the system of equations

We now have a system of two equations:

1. $b + g = 21$
2. $11b + 13g = 251$

Solve for $g$ in terms of $b$:

From the first equation, we can solve for $g$:

$$
g = 21 – b
$$

Substitute $g$ into the second equation:

Now substitute $g = 21 – b$ into the second equation:

$$
11b + 13(21 – b) = 251
$$

Distribute the 13:

$$
11b + 273 – 13b = 251
$$

Simplify the equation:

$$
-2b + 273 = 251
$$

Subtract 273 from both sides:

$$
-2b = -22
$$

Now, divide both sides by -2:

$$
b = 11
$$

Step 3: Find the number of girls

Now that we know $b = 11$, substitute this value into the first equation:

$$
b + g = 21
$$

$$
11 + g = 21
$$

Subtract 11 from both sides:

$$
g = 10
$$

Step 4: Verify the solution

We found that there are 11 boys and 10 girls. Let’s verify by checking the total number of pockets:

• Boys: $11 \times 11 = 121$ pockets.
• Girls: $10 \times 13 = 130$ pockets.
  Total pockets = $121 + 130 = 251$, which matches the given total.

Final Answer:

• There are 11 boys and 10 girls in the class.