Question

Three times the smallest of three consecutive integers is 14 more than twice the largest. Find the largest integer

Answer 1

So y=smallest and x=largest, then since they are consecutive numbers. X-y= 2.
3 times y equals 14 more than 2 times x. So 3y + 14 = 2x -> 14 = 2x-3y


2x-3y= 14
X-y= 2
Adding
3x-4y=16, 3x =16+4y, x = 16/3+4y/3
Plug it back in
(16/3 +4y/3)-y =2, 16/3 +1/3y = 2, 16 +y =6, y = -10
Plug that back in
X-(-10)=2, x+10=2, x = -8
Check answer: so x =-8 & y =-10, then -8-(-10)=2 & 2(-8)-3(-10)=14