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?
suppressing the useless thousands, we have
12a + 20(50-a) = 872
To find the number of aides that may be hired, we need to set up an equation based on the information given. Let's assume the number of teachers is T and the number of aides is A.
According to the given information, there are a total of 50 faculty members, so we can write the equation T + A = 50.
Next, we need to consider the salary of each faculty member. Teachers earn $20,000 a year, so the total salary for teachers will be 20,000T. Aides, on the other hand, earn $12,000 a year, so the total salary for aides will be 12,000A.
The problem states that the total amount to be spent on salaries is $872, 000. So, we can write the equation 20,000T + 12,000A = 872,000.
Now, we have a system of equations:
T + A = 50 ---(Equation 1)
20,000T + 12,000A = 872,000 ---(Equation 2)
To solve this system of equations, we can use substitution or elimination method. However, in this case, it's easier to use substitution.
From Equation 1, we can express T in terms of A by subtracting A from both sides:
T = 50 - A
Now substitute this value of T into Equation 2:
20,000(50 - A) + 12,000A = 872,000
Simplifying the equation:
1,000,000 - 20,000A + 12,000A = 872,000
- 8,000A = 872,000 - 1,000,000
- 8,000A = -128,000
Divide both sides by -8,000:
A = -128,000 / -8,000
A = 16
Therefore, the school may hire 16 aides.