Question

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 ratio 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?

Answer 1

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

We now solve for p:

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

There is 548 professors.