10.If the average of four positive integers is 12, what is the largest possie value of one of those integers?
A.35
B.37
C.40
D.42
E.45
do they have to be different? If not
(1 + 1 + 1 + 45)/4 = 12
if they do have to be different
(1 + 2 + 3 + 42)/4 = 12
To solve this problem, we need to find the largest possible value of one of the four positive integers given that their average is 12.
Let's assume the four positive integers are a, b, c, and d. We know that the average of these four numbers is 12, so we can write the equation:
(a + b + c + d) / 4 = 12
Now, let's solve for the largest possible value. Rearranging the equation, we have:
a + b + c + d = 48
To find the largest possible value, we want to maximize one of the variables (a, b, c, or d) while keeping the sum equal to 48.
Since the integers are positive, we should start by assigning the maximum value to one of the variables (let's say d). Now, the equation becomes:
a + b + c + max(d) = 48
To maximize d, we want to minimize the remaining sum (a + b + c). Assuming a, b, and c are still positive integers, we should assign them the minimum possible values, which are 1 each. So, the equation becomes:
1 + 1 + 1 + max(d) = 48
3 + max(d) = 48
max(d) = 48 - 3
max(d) = 45
Therefore, the largest possible value of one of the integers is 45.
Hence, the answer is E. 45.