To find the total number of students in the math class, we can use the information that 20 students represent 80% of the total number of students. Let's denote the total number of students as \( x \).
From the problem, we can set up the equation:
\[ 0.80x = 20 \]
To find \( x \), we divide both sides by 0.80:
\[ x = \frac{20}{0.80} \]
Calculating this gives:
\[ x = 25 \]
So, the total number of students in the class is 25.
Now, let's check which of the provided equations might represent this situation correctly:
- \( \frac{20 \times 100}{80 \times 100} = \frac{2000}{8000} \)
- \( \frac{80 \times 5}{20 \times 5} = \frac{400}{100} \)
- \( \frac{80 \div 4}{100 \div 4} = \frac{20}{25} \)
- \( \frac{20 \div 1}{80 \div 1} = \frac{20}{80} \)
None of these expressions directly represent the equation of \( 0.80x = 20\), but we can interpret them in connection to finding the proportion.
Option 3 can be rearranged to see the relationship. Let's confirm it:
\[ \frac{80 \div 4}{100 \div 4} = \frac{20}{25} \]
This indicates that \( 20 \) is to \( 25 \) as \( 80 \) is to \( 100 \), which reflects the same proportion. Since \( 20 \) is 80% of \( 25 \), this statement is equivalent to the information given.
Thus, the correct equation that represents the relationship based on the provided options is:
\[ \frac{80 \div 4}{100 \div 4} = \frac{20}{25} \]
This correctly illustrates that 20 students (those with brown hair) is 80% of the total class size (25 students).
3 answers