Question

Tickets are on sale for $1.50 off regular price. Dex buys 6 tickets and spends $51. Write and solve equation for "t" tickets in form p ( x - q ) = r

Answer 1

Let's define the variables clearly.

1. Let \( p \) be the regular price of one ticket.
2. 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 \( p \):

1. Start by distributing the 6:

\[
6p - 9 = 51
\]

2. Add 9 to both sides:

\[
6p = 60
\]

3. 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!