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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?

User Snjezana
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1 Answer

14 votes
14 votes

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.

User Duyker
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