Mrs. Franks is taking her kindergarten class to the circus. She spent a total of $180 for 20 child tickets. If a child ticket is $5 less than an adult ticket, determine the price of an adult and child ticket. Represent this situation with an equation using m as the cost of the adult ticket.(1 point)

Answer 1

Let \( m \) represent the cost of an adult ticket. Given that a child ticket is $5 less than an adult ticket, we can express the cost of a child ticket as \( m - 5 \).

Mrs. Franks purchased 20 child tickets for a total of $180. We can set up the following equation to represent this situation:

\[ 20(m - 5) = 180 \]

This equation can be solved to find the price of the adult ticket. First, distribute the 20:

\[ 20m - 100 = 180 \]

Next, add 100 to both sides:

\[ 20m = 280 \]

Now, divide both sides by 20:

\[ m = 14 \]

So, the cost of an adult ticket is \( m = 14 \) dollars. To find the cost of a child ticket, substitute \( m \) back into the expression for the child ticket:

\[ m - 5 = 14 - 5 = 9 \]

Thus, the prices are:

• Adult ticket: $14
• Child ticket: $9