Math Problem Statement

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?

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:

  1. Total sum of 6 numbers
    The average of 6 numbers is 30.
    So, the total sum of these 6 numbers is:
    6×30=1806 \times 30 = 180

  2. 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:
    4×25=1004 \times 25 = 100

  3. 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:
    3×35=1053 \times 35 = 105

  4. 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:
    Fourth number=(100+105)180=25\text{Fourth number} = (100 + 105) - 180 = 25

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:

  1. What is the formula for calculating the average of a set of numbers?
  2. How does the overlap of sums help in solving problems like this?
  3. Can we solve this problem using algebraic equations instead of averages?
  4. What happens if we change the averages for either the first 4 numbers or the last 3 numbers?
  5. 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