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

System of Equations with Ratio Relationships

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:

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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:

2

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.

3

Final Answer

21

Key Points to Remember

Essential concepts to master this topic
  • Setup: Define variables for both groups, use ratios to connect them
  • Technique: Girls = g, Boys = 3g, so g + 3g = 28
  • Check: 7 girls + 21 boys = 28 total, and 21 ÷ 7 = 3 ✓

Common Mistakes

Avoid these frequent errors
  • Setting up the equation incorrectly with the ratio
    Don't write 'boys = 3 × total students' = 84 boys! This ignores that girls are part of the total. Always remember that both groups together equal the total: girls + boys = 28.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( x - 3 + 5 = 8 - 2 \)

FAQ

Everything you need to know about this question

Why can't I just divide 28 by 3 to get the number of boys?

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Because that ignores the girls! The ratio is between boys and girls, not boys and total students. You need to account for both groups adding up to 28.

How do I know which variable to use for which group?

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Choose the smaller group as your main variable. Since there are 3 times as many boys as girls, girls are fewer, so let g = girls.

What if the problem said 'girls are 3 times boys' instead?

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Then you'd let b = boys and girls = 3b. The setup changes based on which group is described as 'times as many' as the other.

How can I check my ratio is correct?

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Divide the larger number by the smaller: 217=3 \frac{21}{7} = 3 . This confirms there are exactly 3 times as many boys as girls.

What if I get a decimal answer for the number of students?

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Check your work! You cannot have fractional people in a real classroom. A decimal answer usually means there's an error in your setup or calculation.

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