Each of x, y and z is a nonnegative integer such that:

(i) x+y+z = 94, and:
(ii) H = 4x+10y+19z

How many distinct values of H is possible?

We can simplify things talking 4 away from each of x, y and z, since this will remove 94 4's.
H = 0x + 6y + 15z + 4*94
(H-376) = 6y + 15z
(H-376)/3 = 2y + 5z
Call G = (H-376)/3 and we can rephrase the conditions and question as the equivalent:

(i) y+z ≤94, and:
(ii) G = 2y + 5z

How many distinct values of G is (sic) possible?

Edited on October 17, 2014, 6:45 am

Posted by Jer on 2014-10-16 10:16:51