a<b<c<d represent four numbers that can be added in pairs in 6 different ways. If all of the sums are unique and the four smallest sums are 1, 2, 3, and 4, what are all possible values of d?
Here's what I did.
smallest
a+b = 1
a+c = 2
a+d = 3
b+c = 4
b+d = y
c+d = z
largest
(a+d)+(b+c) = 3+4
a+b+c+d = 7
(a+b)+(a+c)+(b+c) = 1+2+4
2a+2b+2c = 7
a+b+c = 7/2
Substitute into previous equation:
(9/2)+d = 7
d = 7-(7/2)
d = (14/2)-(7/2)
d = 7/2
The question asks for all possible values which implies that there is more than one answer. This is the only one answer I could come up with though. Anyone see another possible value for d?
Here's what I did.
smallest
a+b = 1
a+c = 2
a+d = 3
b+c = 4
b+d = y
c+d = z
largest
(a+d)+(b+c) = 3+4
a+b+c+d = 7
(a+b)+(a+c)+(b+c) = 1+2+4
2a+2b+2c = 7
a+b+c = 7/2
Substitute into previous equation:
(9/2)+d = 7
d = 7-(7/2)
d = (14/2)-(7/2)
d = 7/2
The question asks for all possible values which implies that there is more than one answer. This is the only one answer I could come up with though. Anyone see another possible value for d?