In Rockford public schools, teachers with a degree in educat

Question

In Rockford public schools, teachers with a degree in education earn $90,000 a year, $12,000 more than those without. In the last month, six teachers with a degree in education have been hired and four Rockford teachers have been awarded their first degree in education, raising the average yearly earnings of Rockford teachers from $86,000 to $87,000. How many Rockford teachers have a degree in education?

(A) 18
(B) 30
(C) 44
(D) 48
(E) 54

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Official Answer

E

(A) 18
(B) 30
(C) 44
(D) 48
(E) 54

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=89500 The above solve uses weighted average/alligation concepts. --- Harsha GMAT-Club-Forum-bw1rlbmy.png

kevincan · Answer

Alligation (alligator teeth) sure makes quick work of this question !

kevincan · Answer

Edited for clarity

kevincan · Answer

Let all salaries be expressed in thousands of dollars.

Since the original average salary was 86, and 6 teachers were hired at 90, while 4 existing teachers received a 12-thousand-dollar raise:

87(N + 6) = 86N + 6(90) + 4(12)

87N + 522 = 86N + 588

N = 66

Therefore, there are currently 66 + 6 = 72 teachers.

Teachers with a degree in education earn 90 thousand dollars, while teachers without a degree earn 90 − 12 = 78 thousand dollars.

The current average salary is 87 thousand dollars.

Using alligation:

90 ...87..........78

The differences from the average are

90 − 87 = 3 and 87 − 78 = 9.

Therefore, the ratio of teachers with degrees to teachers without degrees is

9 : 3 = 3 : 1.

So 3/4 of the 72 teachers have degrees:

(3/4)(72) = 54

Answer: (E) 54

Kinshook · Answer

In Rockford public schools, teachers with a degree in education earn $90,000 a year, $12,000 more than those without. In the last month, six teachers with a degree in education have been hired and four Rockford teachers have been awarded their first degree in education, raising the average yearly earnings of Rockford teachers from $86,000 to $87,000. How many Rockford teachers have a degree in education?

(A) 18
(B) 30
(C) 44
(D) 48
(E) 54

Show Answer

Official Answer

E

How many Rockford teachers have a degree in education?

Let the number of Rockford teachers having a degree in education be x.
Salary of Rockford teachers having a degree in education = $90,000
Salary of Rockford teachers NOT having a degree in education = $90,000 - $12,000 = $78,000
Average yearly earnings of Rockford teachers = $86,000 
Ratio of Rockford teachers having a degree in education to Rockford teachers NOT having a degree in education = (86000-78000)/(90000-86000) = 8/4 = 2:1
The number of Rockford teachers NOT having a degree in education = x/2

In the last month, six teachers with a degree in education have been hired and four Rockford teachers have been awarded their first degree in education, raising the average yearly earnings of Rockford teachers from $86,000 to $87,000. 
New Rockford teachers having a degree in education = 6
Rockford teachers getting a degree in education = 4

Average yearly earnings of Rockford teachers = $87,000 = (x/2-4)$78,000 + (x+6+4)*$90,000 / (3x/2+6)
39,000x - 3,12,000 + 90,000x + 9,00,000 = 1,30,500x + 5,22,000
x = 44

Initial  number of teachers with an education degree =  44 
 Current  number of teachers with an education degree = 44 + 6 + 4 =  54

IMO E

In Rockford public schools, teachers with a degree in educat

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In Rockford public schools, teachers with a degree in educat

Prep Toolkit

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