SOLUTION: A total of 1,200 teachers attended a mathematics conference. Early bird registration fee is at 2,000 pesos per teacher while regular registration fee costs 2,500 pesos per teacher.

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Question 1176894: A total of 1,200 teachers attended a mathematics conference. Early bird registration fee is at 2,000 pesos per teacher while regular registration fee costs 2,500 pesos per teacher.
a. If x is the number of teachers who registered early, express the total fees collected in terms of x.
b. If 2,825,000 pesos were collected, how many of each type registered?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x+is the number of teachers who registered early
let y+be the number of teachers who registered regularly
x+%2By=1200
y=1200-x.....eq.1
a.
If x+is the number of teachers who registered early, express the total fees collected in terms of x.
2000x
b.
If 2825000 pesos were collected, how many of each type registered?
2000x%2B2500y=2825000..........substitute y from eq.1

2000x%2B2500%281200-x%29=2825000
2000x%2B3000000+-+2500x=2825000
3000000+-+500x=2825000
3000000+-+2825000=500x
175000=500x
x=175000%2F500
x=1750%2F5
x=350-> the number of teachers who registered early
go to eq.1
y=1200-x.....eq.1, substitute x
y=1200-350
y=850-> the number of teachers who registered regularly

the total fees collected from teachers who registered early:2000x=2000%2A350=700000
the total fees collected from teachers who registered regularly:2500y=2500%2A850=2125000


check total:
700000%2B2125000=2825000