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's represent the cost of a child ticket as \( c \) and the cost of an adult ticket as \( m \). According to the problem, we know the following:

1. The price of a child ticket is $5 less than that of an adult ticket: \[ c = m - 5 \]

2. Mrs. Franks bought 20 child tickets for a total of $180: \[ 20c = 180 \]

We can now solve for the cost of a child ticket \( c \): \[ c = \frac{180}{20} = 9 \]

Now that we know the cost of a child ticket is $9, we can substitute this value into the equation for \( c \): \[ 9 = m - 5 \]

Now, we solve for \( m \): \[ m = 9 + 5 = 14 \]

Thus, the prices are:

• Child ticket \( c = 9 \) (which we have verified)
• Adult ticket \( m = 14 \)

In conclusion:

• The price of an adult ticket is $14.
• The price of a child ticket is $9.

The equation that represents this situation is: \[ 20(m - 5) = 180 \]