The average of a set of five different positive integers is 360. The two smallest integers in the set are 99 and 102. What is the largest possible integer in this set?
360*5-sum2= sumlastthree
1800-201=
1599 = sumlast three
But all have to be greater than 102
so let the first two be 102, 103, lowest that they can be.
1599-102-103= last digit.
so figure the last digit.
To find the largest possible integer in the set, we need to determine the sum of the five integers and then subtract the sum of the four known integers (99, 102, and the average of the remaining two integers). Let's break it down step by step:
Step 1: Calculate the sum of the five integers.
Since the average of the five integers is 360, we can multiply the average by 5 to find the sum:
Sum of the five integers = 360 * 5 = 1800.
Step 2: Subtract the sum of the four known integers.
The sum of the four known integers is 99 + 102 + x1 + x2, where x1 and x2 represent the remaining two unknown integers.
1800 - (99 + 102 + x1 + x2) = 1800 - (201 + x1 + x2) = 1800 - (201 + x1 + x2).
Step 3: Simplify the equation and solve for the maximum value of x1 + x2.
1800 - (201 + x1 + x2) = 1599 - (x1 + x2).
To maximize the value of x1 + x2, we need to minimize the value of 1599. Therefore, the largest possible integer in the set is 1599.
So, the largest possible integer in the set is 1599.