The problem asks us to place a number into the empty box so that the average of the remaining seven numbers is 25.

Step-by-Step Solution:

1. Sum of the numbers needed for an average of 25: The average formula is given by: $\text{Average} = \frac{\text{Sum of the numbers}}{\text{Total number of numbers}}$ Since the average of the seven numbers should be 25: $\frac{\text{Sum of the seven numbers}}{7} = 25$ Therefore, the sum of the seven numbers should be: $\text{Sum of the seven numbers} = 25 \times 7 = 175$

2. Sum of all eight numbers: The given numbers are: $11, 19, 23, 26, 27, 28, 34, 35$ The total sum of all eight numbers is: $11 + 19 + 23 + 26 + 27 + 28 + 34 + 35 = 203$

3. Find the missing number: Let $x$ be the number placed into the empty box. The sum of the seven remaining numbers must be 175, so: $\text{Sum of seven numbers} = \text{Total sum} - x$ This gives the equation: $203 - x = 175$ Solving for $x$: $x = 203 - 175 = 28$

Conclusion:

The number to be placed in the box is 28.

Do you have any questions or would you like a detailed breakdown of any part?

Here are 5 related questions to practice:

1. What would the average be if you replaced 35 with 30?
2. If the average were 24 instead of 25, what would the missing number be?
3. What if the average were 26, what would the missing number be?
4. How does changing one number affect the average of a set?
5. Can the number to be placed in the box ever be smaller than 11?

Tip: To calculate averages faster, focus on sums and division!