Question

Children's tickets to a local play cost $\$1.50$ less than adult tickets. At one performance 325 children tickets and 175 adult tickets were sold for a total of $\$3512.50$. How many dollars did an adult ticket cost?

Answer 1

Answer:

  $8.00

Step-by-step explanation:

The problem statement gives two relations between the prices of two kinds of tickets. These can be used to write a system of equations for the ticket prices.

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setup

Let 'a' and 'c' represent the prices of adult and children's tickets, respectively. The given relations can be expressed as ...

  a - c = 1.50 . . . . . . . adult tickets are $1.50 more

  175a +325c = 3512.5 . . . . . total revenue from ticket sales.

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solution

We are only interested in the price of an adult ticket, so we can eliminate c to give one equation we can solve for 'a'. Using the first equation, an expression for c is ...

  c = a -1.50

Substituting that into the second equation, we have ...

  175a +325(a -1.50) = 3512.50

  500a -487.50 = 3512.50 . . . . . . simplify

  500a = 4000 . . . . . . add 487.50

  a = 8 . . . . . . . . . divide by 500

An adult ticket costs $8.