The average of five consecutive integers is 13. One of the integers is removed and the sum of the remaining integers is 53. What is the value of the integer that was removed??
n + n+1 + n+2 + n+3 + n+4
= 5 n + 10
so
(5n+10)/5 = 13
5n+10 = 65
5 n = 55
n = 11
so
11 , 12, 13 , 14, 15
old sum was 65
new sum is 53
difference is 12
so
12
Thank you Damon.
You are welcome.
To solve this problem, we can use algebraic representation. Let's assume that the five consecutive integers are x, x+1, x+2, x+3, and x+4.
According to the given information, the average of these five integers is 13. We can calculate the sum of these integers by multiplying the average by the number of integers (5).
Sum of the integers = Average * Number of integers
Sum of the integers = 13 * 5 = 65
However, one of the integers is removed, and the sum of the remaining integers is 53. We can represent this using an equation:
Sum of remaining integers = Sum of all integers - Value removed
53 = 65 - Value removed
To find the value of the integer that was removed, we rearrange the equation:
Value removed = 65 - 53
Value removed = 12
Therefore, the value of the integer that was removed is 12.