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?

(In reply to Simplified, no solution by Jer)

Jer, as you demonstrated and indicated,
"(H-376)/3 = 2y + 5z" and "(ii) G = 2y + 5z"
I believe, you meant "Call G = (H-376)/3 ...."

As had Charlie, but without the added analysis, I ran a short computer coded routine and came up with the same number as he.
There are 465 distinct possible values of H. With anywhere from 1 to 19 values of x,y,z for each value of H.

Edited on October 16, 2014, 10:57 am

Posted by Dej Mar on 2014-10-16 10:51:57