Math Problem Statement
There are 450 students in the school of academic studies. The ratio of female students to male students is 5:4, how many male and female students are there in the school?
Solution
To solve this problem, we can use the given ratio of female to male students, which is 5:4. Let's break this down step by step.
Step 1: Set Up the Ratio
Let the number of female students be and the number of male students be , where is a common multiplier.
Step 2: Use the Total Number of Students
We know the total number of students is 450. Therefore, we can write the equation:
Step 3: Simplify the Equation
Combine the terms on the left-hand side:
Step 4: Solve for
Divide both sides by 9 to find :
Step 5: Find the Number of Female and Male Students
Now that we know :
- The number of female students is .
- The number of male students is .
Final Answer:
- Number of female students: 250
- Number of male students: 200
Would you like more details, or do you have any questions?
Here are some related questions to consider:
- What would the ratio be if there were 300 female students?
- If the ratio changed to 3:2, how many male students would there be?
- How many students would there be if the ratio remained 5:4 but there were 300 male students?
- If 10 male students transferred out, what would the new ratio of females to males be?
- How would the total number of students change if both the female and male student numbers doubled?
Tip: When working with ratios, always remember to check if the total matches the sum of the parts before finalizing your answer.
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Math Problem Analysis
Mathematical Concepts
Ratios
Basic Algebra
Formulas
Ratio Formula: a/b = x/y
Total Number of Students: a + b = Total
Theorems
Proportionality Theorem
Suitable Grade Level
Grades 5-7
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