a<b<c<d. if a+b+c=395 and b+c+d=1001.Then find the value of d.

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We are given a+b+c=395, b+c+d=1001 and a<b<c<d and we are asked to find the value of d:

As stated, d can take on a range of values.

Subtract the two equations:

a+b+c   =395
-a      +d=606   or


This isn't the whole story as we also know that a<b<c<d.

Assuming that a,b,c,d are integers there is a clear upper bound on a: a<130. (If a=131, then b+c=264 ==> b=c=132 but b<c.)

There is also a lower bound on a. (Unless a,b,c,d are natural numbers, in which case the lower bound is a>0.) If a<-271 then d becomes too small. e.g. if a=-272, then b+c=667 and the smallest that c can be is 334, but d=334 which contradicts c<d.


Assuming a,b,c,d are integers then the value of d depends on a ; d=606+a where -272<a<130 (so that 334<d<736).

If a,b,c,d are natural numbers then d=606+a where 0<a<130 and 606<d<736.



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