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he occupations of biomedical​ engineers, skin care​ specialists, and physician assistants are among the 1010 with the largest growth from 2008 to 2018. The number of physician assistant jobs will grow 55 thousand less than 33 times the number of biomedical engineer jobs. The number of skin care specialist jobs will grow 1313 thousand more than half the number of biomedical engineer jobs. If the total growth of these three jobs is predicted to be 6262 ​thousand, find the predicted growth of each job.

Answer :

Let x = growth of physician assistants (PA)
Let y =  growth of biomedical engineers (BE)
Let z =  growth of skin care specialists (SC)

The growth of PA jobs is 55K less than 33 times the growth of BE jobs. Therefore
x = 33y - 55                (1)

The growth of SC jobs is 1313K more than 12 of BE jobs. Therefore
z = (1/2)y + 1313           (2)

Total growth is 6262K. Therefore
x + y + z = 6262          (3)

Substitute (1) and (2) into (3).
33y - 55 + y + y/2 + 1313 = 6262
34.5y + 1258 = 6262
34.5y = 5004
y = 145.044 ≈ 145 K

From (1), obtain
x = 33*145.044 - 55 = 4731.4 K

From (2) obtain
z = 0.5*145 + 1313 = 1385.5 K

Answer:
PA grows by 4731.4 K
BE grows by 145.0 K
SC grows by 1385.5 K

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