the product of two whole numbers is 48. find their greatest possible sum. what is the least sum.?
To find the greatest possible sum of two whole numbers whose product is 48, we need to find the pair of numbers with the largest sum.
Let's list all the possible pairs of numbers whose product is 48:
1 × 48 = 48
2 × 24 = 48
3 × 16 = 48
4 × 12 = 48
6 × 8 = 48
Now let's calculate the sum for each pair:
1 + 48 = 49
2 + 24 = 26
3 + 16 = 19
4 + 12 = 16
6 + 8 = 14
Thus, the greatest possible sum is 49.
To find the least possible sum of two whole numbers whose product is 48, we need to find the pair of numbers with the smallest sum.
By examining the list of pairs above, we can see that the smallest sum is 6 + 8 = 14.
So, the greatest possible sum is 49, and the least possible sum is 14.
To find the greatest possible sum of two whole numbers whose product is 48, we need to determine which two whole numbers have a product of 48 and find the largest sum among them. Similarly, to find the least sum, we need to find the smallest sum among the same set of numbers.
Step 1: Determine the factors of 48
The factors of 48 are the numbers that can evenly divide 48 without leaving a remainder. To find the factors, you can start by dividing 48 by 1, then 48 by 2, and continue until you reach the square root of 48. This helps us find pairs of factors.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Step 2: Find the pairs of factors whose product is 48
To find the pairs of factors that equal 48, we can pair up the factors. Starting with the smallest factor, pair it with the largest factor and work our way inward. For example, pair 1 with 48, 2 with 24, 3 with 16, and so on.
Pairs of factors: (1, 48), (2, 24), (3, 16), (4, 12), (6, 8)
Step 3: Calculate the sums for each pair
To find the sum for each pair, simply add the two numbers together (the factors).
Sum for each pair:
(1, 48) = 1 + 48 = 49
(2, 24) = 2 + 24 = 26
(3, 16) = 3 + 16 = 19
(4, 12) = 4 + 12 = 16
(6, 8) = 6 + 8 = 14
Step 4: Determine the greatest and least sums
To find the greatest possible sum, we need to select the largest sum among the pairs.
Greatest sum = 49
To find the least sum, we need to select the smallest sum among the pairs.
Least sum = 14
So, the greatest possible sum of the two whole numbers whose product is 48 is 49, and the least possible sum is 14.
I started it as a simple calculus question ...
first number: x
2nd number : 48/x
sum = x + 48/x
d(sum)/dx = 1 - 48/x^2
= 0 for a min of sum
x^2 = 48
x = √48 = appr 9
but you want the numbers to be whole numbers
so possible ordered pairs:
(1,48)
(2,24)
(3,16)
(4,12)
(6,8)
least sum = 6+8 = 14
largest sum =1+48 = 49