Let the number of biomedical engineers be b, the number of skin care specialists be s, and the number of physician assistants be p.
Given that the number of physician assistant jobs will grow 1 thousand less than 3 times the number of biomedical engineer jobs. This implies
3b - p = 1,000 - - - - - - - - (1)
Given that the number of skin care specialist jobs will grow 13 thousand more than half the number of biomedical engineer jobs. This implies
[tex]s- \frac{1}{2} b=13,000[/tex] - - - - - - - - (2)
Given that the total growth of these three jobs is predicted to be 57 thousand. This implies that
b + s + p = 57,000 - - - - - - - - (3)
We solve the three equations simultaneously as follows:
From (1): p = 3b - 1,000 - - - - - - - - (4)
From (2): [tex]s= \frac{1}{2} b+13,000[/tex] - - - - - - - - (5)
Putting (4) and (5) into (3), we have
[tex]b+\frac{1}{2} b+13,000+3b - 1,000=57,000 \\ \\ \frac{9}{2} b=57,000-13,000+1,000=45,000 \\ \\ b= \frac{45,000\times2}{9} =10,000[/tex]
From (4): p = 3(10,000) - 1,000 = 30,000 - 1,000 = 29,000
From (5): [tex]s= \frac{1}{2} (10,000)+13,000=5,000+13,000=18,000[/tex]
Therefore, the growth of biomedical engineers is 10,000.
The growth of skin care specialists is 29,000, and
The growth of physician assistants is 18,000.
