Let's define the variables clearly.
- Let \( p \) be the regular price of one ticket.
- The discount on the ticket price is $1.50, which means the sale price of one ticket is \( p - 1.50 \).
Dex buys 6 tickets for a total of $51. Therefore, we can express this situation with the following equation:
\[ 6(p - 1.50) = 51 \]
Now, we can simplify and solve the equation for \( p \):
- Start by distributing the 6:
\[ 6p - 9 = 51 \]
- Add 9 to both sides:
\[ 6p = 60 \]
- Divide both sides by 6:
\[ p = 10 \]
Now, we know the regular price of one ticket is $10.
To rewrite the original equation in the form \( p(x - q) = r \):
- Here, \( p \) is 6,
- \( x \) would be the price per ticket (which is \( p - 1.50 \)),
- \( q \) would be 1.50,
- and \( r \) is 51.
Thus, we can express it as:
\[ 6 \left( (p - 1.50) \right) = 51 \]
This matches the required form where you have the number of tickets times the price minus the discount equals the total spent.
In terms of the values we found:
\[ 6 \left( (10 - 1.50) \right) = 51 \]
So the solution and representation are consistent and correct!
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