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

We can determinate there is 548 professors.

Step-by-step 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 ((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 = (40,415,000)/(73,750)  = 548`

There is 548 professors.