SOLUTION: What is the largest possible product for 2 even integers whose sum is 34 ? F.64 G.68 H.120 J.240 K.288

Question 324928: What is the largest possible product for 2 even integers whose sum is 34 ?
F.64
G.68
H.120
J.240
K.288

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the largest possible product for 2 even integers whose sum is 34 ?
--------------------------------
If the numbers are even they must be multiples of 2.
---------------------
(2x)+(2y) = 34
x+y = 17
-----
product = 2x*2y = 4xy
Substitute for "y" to get:
---
product = 4x(-x+17) = -4x^2+68x
---
Max occurs when x = -b/2a = -68/(-8) = 8.5
---
2x = 2(8.5) = 17
Note: 2x is not an even number
---
Since x+y = 17, y = 8.5
2y = 17
Note: 2y is not an even number
----
The even number sum must be 16 and 18
The max product must be (16)(18)
==========================================
Cheers,
Stan H.

F.64
G.68
H.120
J.240
K.288

RELATED QUESTIONS
what is the largest possible product for two odd integers whose sum is 30? (answered by Alan3354)

What is the largest possible product of a set of positive integers whose sum is... (answered by jsmallt9)

how do I figure out the largest possible product of two even integers whose sum is... (answered by ikleyn)

find two consecutive even integers whose product is... (answered by kirubakaran)

find two consecutive even integers whose product is... (answered by jim_thompson5910)

Find the largest possible values for a set of three consecutive even integers whose sum... (answered by stanbon)

What is the smallest possible product for two positive integers whose sum is 26? (answered by richwmiller)

What is the largest number which is the product of positive integers whose sum is... (answered by swincher4391)

what is the largest of three consecutive even integers whose sum is... (answered by checkley77)