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the marching band is having a show to raise at least $1000 forntheir upcoming trip. Each adults is $6 and students $4. The auditorium has a maxium capacity of 200 people.

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This question is incomplete. I assume that you are looking for the number of adults and students.

Let a = adult

Let s = student

6a + 4s = 1000...A
a + s = 200...B

We have a system of linear equations in two variables, the variables a and s.

You can select any variable of choice to represent the adults and students.

Solve equation B for a or s (your choice).

a + s = 200

Solve for a or s (your choice).

s = 200 - a

Plug into equation A to find the value of a.

6a + 4(200 - a) = 1000

6a + 800 - 4a = 1000

6a - 4a = 1000 - 800

2a = 200

a = 200/2

a = 100

There are 100 adults.

Plug a = 100 into EITHER equation A or B to find students.

a + s = 200

100 + s = 200

s = 200 - 100

s = 100

There are also 100 students.

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