Question

students at springfield school can join either the orchestra or the marching band. students cannot join both groups. how many 7th graders are in the band?
orchestra band total
6th grade 24 18 42
7th grade 32 ? ?
8th grade ? 27 72
total 101 69 170
24 students
45 students
56 students
69 students

Explanation:

Step1: Find total band students

The total number of students in the band across all grades is given as 69.

Step2: Subtract known band students

We know the number of 6th graders in the band is 18 and 8th graders in the band is 27. So we calculate the number of 7th graders in the band by subtracting the sum of 6th and 8th graders in the band from the total band students.
First, find the sum of 6th and 8th graders in the band: $18 + 27 = 45$.
Then, subtract this sum from the total band students: $69 - 45 = 24$? Wait, no, wait. Wait, total band is 69. 6th band:18, 8th band:27. So 7th band = 69 - 18 -27. Let's recalculate: 18 +27 =45. 69 -45 =24? But wait, let's check the total 7th grade. Wait, maybe I made a mistake. Wait, total orchestra is 101. 6th orchestra:24, 7th orchestra:32, so 8th orchestra is 101 -24 -32 =45. Then total 8th grade is 72, so 8th band is 72 -45 =27, which matches. Then total band is 18 (6th) + x (7th) +27 (8th) =69. So 18 +27 +x =69. 45 +x =69. x=69-45=24. Wait, but the options have 24 as an option. Wait, but let me check again. Wait, the total number of students is 170. Total orchestra 101, total band 69, 101+69=170, which matches. 6th grade total:24+18=42, which matches. 8th grade total:45 (orchestra) +27 (band)=72, which matches. Then 7th grade total:170 -42 -72=56. Then 7th grade orchestra is 32, so 7th grade band is 56 -32=24. Yes, so the number of 7th graders in the band is 24. Wait, but the options have 24 as an option. Wait, but the options are: 24,45,56,69. So the correct answer is 24. Wait, but let me check again. Wait, 7th grade total: total students 170. 6th total 42, 8th total 72. So 170 -42 -72=56. So 7th grade total is 56. 7th grade orchestra is 32, so band is 56-32=24. Yes. So the answer is 24.

Answer:

24 students (the option with "24 students")