Let n be the smallest of these integers. The other two are then n + 2 and n + 4.
"triple of the sum of thrice the third one and twice the first one is equal to 291" is a long-winded way of saying
3 (3 (n + 4) + 2n) = 291
Solve for n :
3 (3n + 12 + 2n) + 291
3 (5n + 12) = 291
15n + 36 = 291
15n = 255
n = 17
Then the greatest of the three integers is n + 4 = 21.
