Solve for Boys: Finding 3x Girls in a 28-Student Class Problem

Question

In eighth grade there are a total of 28 students.

If there are 3 times as many boys as girls in the class.

Determine how many boys there are in total:

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Define variables based on the problem.
  • Step 2: Set up an equation using the given total and ratio.
  • Step 3: Solve the equation to find the number of girls.
  • Step 4: Calculate the number of boys using the ratio.

Now, let's work through each step:
Step 1: Let g g be the number of girls. According to the problem, there are 3 times as many boys as girls, so the number of boys is 3g 3g .
Step 2: Since the total number of students is 28, we set up the equation:
 g+3g=28\ g + 3g = 28
Step 3: Combine like terms to simplify the equation:
 4g=28\ 4g = 28
To solve for g g , divide both sides by 4:
 g=284=7\ g = \frac{28}{4} = 7
Step 4: Calculate the number of boys as 3g 3g :
 3g=3×7=21\ 3g = 3 \times 7 = 21

Therefore, the solution to the problem is 21 boys in the class.

Answer

21