A new elementary school will have 50 faculty members. Some will be teachers and the rest will be aides. At this school, teachers will earn 20,000 dollars a year and the aides 12,000 dollars. The total amount to be spent on salaries is $872, 000. How many aides may they hire?
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that answer says there are negative anoint of aides and there isnt
anoint???
Not sure what you mean by "the answer"
If you mean the solution to the equation
12a + 20(50-a) = 872
then it is clear that there are 16 aides.
If your "answer" is the supposed answer key, then it is clearly wrong, as there cannot be a negative number of aides.
To solve this problem, we can set up a system of equations to represent the given information.
Let's assume the number of teachers is "T" and the number of aides is "A".
From the problem, we are given the following information:
1. Teachers earn $20,000 a year.
2. Aides earn $12,000 a year.
3. The total amount to be spent on salaries is $872,000.
Based on this information, we can set up the following equations:
Equation 1: T + A = 50 (since the total number of faculty members is 50)
Equation 2: 20,000T + 12,000A = 872,000 (since the total salary amount is $872,000)
To solve this system of equations, we can use substitution or elimination method. Let's solve it using the elimination method:
Multiply Equation 1 by 12,000 to make the coefficients of "A" in both equations the same:
12,000(T + A) = 12,000(50)
12,000T + 12,000A = 600,000
Now, subtract Equation 2 from the above equation:
(12,000T + 12,000A) - (20,000T + 12,000A) = 600,000 - 872,000
12,000T + 12,000A - 20,000T - 12,000A = -272,000
Combine like terms:
-8,000T = -272,000
Divide both sides by -8,000:
T = (-272,000) / (-8,000)
T = 34
Now substitute the value of T into Equation 1 to find the number of aides (A):
34 + A = 50
A = 50 - 34
A = 16
Therefore, they may hire 16 aides.