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As a fundraising event, a club sold tickets to a special viewing of a classic movie. The club sold all 800 seats in the school’s auditorium. The tickets were three different prices: $2.50 for children under 12 years old, $3.50 for youth between 12 and 18 years old, and $5.00 for adults. The total amount of money taken in was $2937.50, and there were 4 times as many youth tickets as children’s tickets sold.

Respuesta :

Using a system of equations, the amounts of tickets sold are given as follows:

  • Children: 125.
  • Youth: 500.
  • Adult: 175.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given by:

  • Variable x: Number of children tickets sold.
  • Variable y: Number of youth tickets sold.
  • Variable z: Number of adult tickets sold.

The club sold all 800 seats in the school’s auditorium, hence:

x + y + z = 800.

The total amount of money taken in was $2937.50, hence:

2.5x + 3.5y + 5z = 2937.50.

There were 4 times as many youth tickets as children’s tickets sold, hence:

y = 4x.

Replacing the last equation into the first, we have that:

x + 4x + z = 800 -> z = 800 - 5x.

Replacing into the second, we solve for x.

2.5x + 3.5y + 5z = 2937.50.

2.5x + 3.5(4x) + 5(800 - 5x) = 2937.50.

8.5x = 1062.5.

x = 1062.5/8.5.

x = 125.

The other amounts are:

  • y = 4x = 4(125) = 500.
  • z = 800 - 5x = 800 - 5(125) = 175.

The amounts were:

  • Children: 125.
  • Youth: 500.
  • Adult: 175.

More can be learned about a system of equations at https://brainly.com/question/24342899

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