Question

Two hundred tickets were sold for the high school concert for a total income of $475. Student tickets were sold for $2 each and adult tickets for $3 each. How many adult tickets were sold?

Answer 1

Let's define the following variables:

x = number of adult tickets sold

$3 = price per adult ticket

y = number of student tickets sold

$2 = price per student ticket

If a total of 200 tickets were sold, then we can say that x + y = 200. This will be our equation 1.

If the total income is $475, then 3x + 2y = 475. This will be our equation 2.

So, we have a system of equations here.

`\begin{gathered} x+y=200 \\ 3x+2y=475 \end{gathered}`

Let's solve for the value of x using the substitution method.

1. Let's rewrite equation 1 into y = 200 - x.

2. Let's replace the "y" variable in equation 2 with "200 - x".

`3x+2y=475`
`3x+2(200-x)=475`

3. Let's solve for x.

Multiply 2 by the terms inside the parenthesis.

`3x+400-2x=475`

Combine similar terms like 3x and -2x.

`(3x-2x)+400=475`
`x+400=475`

Subtract 400 on both sides of the equation.

`x+400-400=475-400`
`x=75`

The value of x is 75.

Since x is the number of adult tickets sold, then there were 75 adult tickets sold for the high school concert.