Avg age of X number of adults in a class is 30yrs. If 12 new adults with avg age of 32 joined with them then the avg age increases by one. Find X?

let ad1 be adult 1 and so on

ad1 + ad2 +ad3 + .... + ad(x) = 30x ------------------------------------------(1)

ad(x+1)+ad(x+2) ....... + ad(x+11)+ad(x+12) = 32*12

ad1+ad2+ad3+.................+ad(x+11)+ad(x+12) = 31x + 372 -------------------------(2)

(2) - (1)

ad(x+1) + ad(x+2) ....... + ad(x+11) + ad(x+12) = 31x + 372 - 30x = x + 372

==> x+372 = 384

==> x = 384 - 372 = 12

so total number of adults = 12

please approve if the answer is correct  !!