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tensa zangetsu [6.8K]
3 years ago
15

A given university has an average professor pay of $40,000 a year and an average administrator pay of $45,000 per year. If the r

atio of professors to administrators is 4 to 3, and the total pay for professors and administrators in a year is $40,415,000, how many professors does the college have?
Business
1 answer:
harina [27]3 years ago
5 0

Answer:

We can determinate there is 548 professors.

Explanation:

A professor is paid 40,000 while and administrator is paid 45,000

we know that the sum of wages is 40,415,000

and the proportion for professors is 4/3 so admin should be 3/4

We can now construct and equation system.

40,000p + 45,000a = 40,415,000\\where:\\p = professor\\a = administrators

We know plug the value of admin to professor and sove for p.

40,000p + 45,000 (\frac{3}{4}p) = 40,415,000

we multiply 45,000 by 3/4 and add it to the 40,000

45,000 x 3/4 = 33,750

40,000 + 33,750 = 73,750

<u>We now solve for p:</u>

p = \frac{40,415,000}{73,750}  = 548

There is 548 professors.

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