# There exists integer x,y,z satisfying 28x+30y+31z=365 then the value of z-2x for some such triplet is?

Jul 25, 2018

In English calendar year (not leapyear) of 365 days there exist one month of 28 days ,4 months of 30 days and 7 months of 31days .

So $28 \times 1 + 30 \times 4 + 31 \times 7 = 365$

Comparing with given relation

$28 x + 30 y + 31 z = 365$

We get $x = 1 , y = 4 \mathmr{and} z = 7$

Hence $z - 2 x = 7 - 2 \cdot 2 = 5$