Question

One half plus 8 of the students at Monroe School are in band. 12 less than 2/3rds of the students are in orchestra. If the same number of students that are in band are in orchestra, how many students are there at the Monroe School?

Answer 1

120 students

Explanation:

Let number of students in Monroe School be N

• "One half plus 8 of the students at Monroe School are in band."
  
  
  `\rightarrow (N)/(2) + 8 \text{ students are in band}`

• "12 less than 2/3rds of the students are in orchestra"
  
  
  `\rightarrow (2)/(3) N -12 \text{ are in orchestra}\\\\`

• These numbers are equal:
  
  `(N)/(2) + 8 = (2)/(3) N -12`
  
• Multiply throughout by 6
  
  `6 \cdot (N)/(2) + 6 \cdot 8 = 6 \cdot (2)/(3)N - 6 \cdot 12 \\\\3N + 48 = 4N - 72\\\\48 + 72 = 4N - 3N\\\\120 = N\\\\or\\\\N = 120\\\\\\`

Therefore there are 120 students at Monroe School