Math Problem Statement
Solution
The problem is in Hindi and translates to:
"There are 6 numbers with an average of 30. If the average of the first 4 numbers is 25 and the average of the last 3 numbers is 35, what will the fourth number be?"
Step-by-step solution:
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Total sum of 6 numbers
The average of 6 numbers is 30.
So, the total sum of these 6 numbers is:
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Sum of the first 4 numbers
The average of the first 4 numbers is 25.
So, the total sum of the first 4 numbers is:
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Sum of the last 3 numbers
The average of the last 3 numbers is 35.
So, the total sum of the last 3 numbers is:
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Finding the fourth number
From the total sum of 6 numbers, the sum of the first 4 numbers and the last 3 numbers overlap at the fourth number.
Hence, we calculate the fourth number as:
Final Answer:
The fourth number is 25.
Do you want further clarification or detailed explanation for any step?
Here are 5 related questions to enhance understanding:
- What is the formula for calculating the average of a set of numbers?
- How does the overlap of sums help in solving problems like this?
- Can we solve this problem using algebraic equations instead of averages?
- What happens if we change the averages for either the first 4 numbers or the last 3 numbers?
- How would this problem change if we had a different total number of values?
Tip: When solving problems involving averages and overlapping groups, carefully track which groups are included in the totals to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Averages
Basic Arithmetic
Overlap of Sums
Formulas
Average = Total Sum / Number of Elements
Theorems
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Suitable Grade Level
Grades 6-8