Aprivate school $860,000 in one year to pay all of its teachers and administrators. the school has a total of twenty-four teachers and administrators combined. if teachers make $35,000 per year and administrators make $40,000 per year, how many teachers and how many administrators does the school have?

Hi there!

Let t be the number of teachers
Let a be the number of administrators

t+a=24
35,000t+40,000a=860,000
a=24-t
35,000t+40,000(24-t)=860,000
35,000t+960,000-40,000t=860,000
35,000t-40,000t=860,000-960,000
-5,000t=-100,000
t=-100,000/-5,000
t=20
a=24-t
a=24-20
a=4

Therefore there are 4 administrators and 20 teachers. 

Hope this helps!