The average of a set of numbers is 50. If one number is removed, the average bec
Practice Questions
Q1
The average of a set of numbers is 50. If one number is removed, the average becomes 48. What was the number that was removed?
50
52
54
56
Questions & Step-by-Step Solutions
The average of a set of numbers is 50. If one number is removed, the average becomes 48. What was the number that was removed?
Step 1: Understand that the average of a set of numbers is calculated by dividing the total sum of the numbers by the number of items.
Step 2: Let 'n' be the number of items in the original set.
Step 3: Since the average is 50, the total sum of the numbers can be calculated as 50 times n, which is 50n.
Step 4: When one number is removed, the number of items becomes (n - 1).
Step 5: The new average after removing one number is 48, so the new total sum can be expressed as 48 times (n - 1), which is 48(n - 1).
Step 6: Set up the equation: The original total sum (50n) minus the removed number (let's call it x) equals the new total sum (48(n - 1)). This gives us the equation: 50n - x = 48(n - 1).
Step 7: Simplify the equation: 50n - x = 48n - 48.
Step 8: Rearrange the equation to find x: x = 50n - 48n + 48.
Step 9: Combine like terms: x = 2n + 48.
Step 10: To find the value of n, we can use the fact that when one number is removed, the average drops to 48. We can substitute n with a value that makes sense. If we assume n = 25 (for example), then x = 2(25) + 48 = 50 + 48 = 52.
Step 11: Therefore, the number that was removed is 52.
