The occupations of biomedical engineers, skin care specialists, and physician assistants are among the 15 with the largest growth from 2008 to 2018. the number of physician assistant jobs will grow 2 thousands less than 3 times the number of biomedical engineer jobs. the number of skin care specialist jobs will grow 13 thousand more than half the number of biomedical engineer jobs. if the total growth of these three jobs is predicted to be 65 thousand, find the predicted growth of each job.

Let the growth in the number of biomedical jobs is x thousand,

Thus, According to the question,

The number of physician assistant jobs will grow = 3 x - 2000

The number of skin care specialist jobs will grow = 1/2 x + 13,000,

Thus, the total growth in the number of these three occupation,

= x + 3 x - 2000 + 1/2 x + 13000

= 9/2 x + 11000

Again, according to the question,

9/2 x + 11000 = 65,000

9/2 x = 54,000

9 x = 108000

x = 12,000

Hence, the growth in the number of biomedical jobs = x = 12,000

The number of physician assistant jobs will grow = 3 x - 2000 = 3 × 12000 - 2000 = 36000 - 2000 = 34000

The number of skin care specialist jobs will grow = 1/2 x + 13,000 = 1/2 × 12000 + 13000 =  6000 + 13000 = 19000