Last Updated on May 3, 2023
In an increasing sequence of 10 consecutive integers…
Solution:
In solving this problem we must first remember that when we have 10 consecutive integers we can display those in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
Integer 4: x + 3
Integer 5: x + 4
Integer 6: x + 5
Integer 7: x + 6
Integer 8: x + 7
Integer 9: x + 8
Integer 10: x + 9
We are given that the sum of the first 5 integers is 560. This means that:
x + x+1 + x+2 + x+3 + x+4 = 560
5x + 10 = 560
5x = 550
x = 110
The sum of the last 5 integers can be expressed and simplified as:
x+5 + x+6 + x+7 + x+8 + x+9 = 5x + 35
Substituting 110 for x yields:
(5)(110) + 35 = 585.
Answer: A
Note: Alternatively, because both equations have 5x in common, we know that the difference between the sum of the first five numbers and the sum of the last five numbers is the difference between (1+2+3+4) and (5+6+7+8+9). Since 35 – 10 = 25, the sum of the last 5 is 585, which is 25 more than 560.
