1.)Matt's Oak Superstore has exactly three times as many large oak desks as small oak desks in its inventory. If the store only sells these two types of desks, which could be the total number of desks in stock?
2.) If Set M contains 4 positive integers whose avarge is 7, then what is the largest number that set M could contain?
1.) To find the possible total number of desks in stock, we need to determine the relationship between the number of large oak desks and small oak desks.
Let's assume the number of small oak desks is represented by 'x'. According to the information given, the number of large oak desks is three times the number of small oak desks, which can be represented as '3x'.
Therefore, the total number of desks in stock would be the sum of the small oak desks and the large oak desks: x + 3x = 4x.
Based on this, the total number of desks must be a multiple of 4. So, any number that is divisible by 4 could be the total number of desks in stock.
2.) To find the largest number that Set M could contain, we need to use the concept of the average.
Let's assume the four positive integers in Set M are represented by 'a', 'b', 'c', and 'd'. According to the information given, the average of these four integers is 7.
The formula for the average is: (a + b + c + d) / 4 = 7.
To find the largest number, we want to maximize the sum of all the integers in Set M.
Let's assume the largest number in Set M is 'p'. Considering that 'p' should be as large as possible, we can assign it the value of 7. This allows the remaining three numbers to be minimized while still maintaining an average of 7.
So, the largest number that Set M could contain is 7.