Question
the product of two whole numbers is 48. find their greatest possible sum. what is the least sum.?
Answers
Reiny
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
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