The all-city band is made up of students from 3 schools. bayside, lincoln, and hendricks. 20 students are in the all-city band. 5 students come from bayside. lincoln has 1 more student in the band than hendricks. how many students in the all-city band come from each school?
bayside=5
lincoln x+1
hendricks=x
band 20=5+x+x+1
20=2x+6
14=2x
7=x
so hendricks has 7 and lincoln has 8
Hendricks --- x
Lincoln ----- x+1
Bayside ---- 5
solve for x
x + x+1 + 5 = 20
2x+6=20
2x=14
x=7
then plug it back in to hendricks,lincoln, and bayside
To solve this problem, let's break it down step by step:
Step 1: Identify the given information.
- There are a total of 20 students in the all-city band.
- Bayside has 5 students in the band.
- Lincoln has 1 more student in the band than Hendricks.
Step 2: Assign variables to the unknowns.
- Let's assume the number of students from Hendricks is x.
- Since Lincoln has 1 more student than Hendricks, the number of students from Lincoln is x + 1.
Step 3: Set up the equation.
- The total number of students in the all-city band is the sum of the students from each school: 5 (from Bayside) + x (from Hendricks) + (x + 1) (from Lincoln) = 20
Step 4: Solve the equation.
- Combine like terms: 5 + x + x + 1 = 20
- Simplify: 2x + 6 = 20
- Subtract 6 from both sides: 2x = 14
- Divide both sides by 2: x = 7
Step 5: Calculate the number of students from each school.
- Bayside has 5 students.
- Hendricks has 7 students.
- Lincoln has 7 + 1 = 8 students.
Answer: In the all-city band, 5 students come from Bayside, 7 students come from Hendricks, and 8 students come from Lincoln.