A community organization was raising money by hosting a concert. The theater that they held the concert in could only seat 320 people. They decided to charge $8 for an adult and $5 for a child. If they hopes to raise $2000, what is the greatest number of children that could attend

Question

Mathematics

Marisa Liu

6 September, 22:05

A community organization was raising money by hosting a concert. The theater that they held the concert in could only seat 320 people. They decided to charge $8 for an adult and $5 for a child. If they hopes to raise $2000, what is the greatest number of children that could attend

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Answers (1)

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Malik Walton · Answer 1

186 children could attend.

The system of equations would be

A+C=320

8A+5C=2000

Solve the first equation for A by subtracting C from both sides:

A+C-C=320-C

A=320-C

Substitute this into the second equation:

8 (320-C) + 5C=2000

2560-8C+5C=2000

2560-3C=2000

Subtract 2560 from both sides:

2560-3C-2560=2000-2560

-3C=-560

Divide both sides by - 3:

-3C/-3 = - 560/-3

C = 186.7

Since we cannot have 0.7 of a child, there can be 186 children.