Question

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

Answer 1

To solve the problem, let's first define the variables and break down the information given in the question.

Let:
- \( p \) = the regular price of each ticket
- \( t \) = the number of tickets Dez buys, which is 6
- \( r \) = the total amount spent by Dez, which is $51
- The discounted price per ticket is \( p - 1.50 \)

We can now set up the equation based on the details given. Since Dez is buying 6 tickets at the discounted price, we can express the total cost as:

\[
t \cdot (p - 1.50) = r
\]

Substituting the values for \( t \) and \( r \):

\[
6 \cdot (p - 1.50) = 51
\]

Now, we can simplify and solve for \( p \):

1. Distribute the 6:

\[
6p - 9 = 51
\]

2. Add 9 to both sides:

\[
6p = 51 + 9
\]
\[
6p = 60
\]

3. Divide by 6:

\[
p = 10
\]

Now we have found the regular price of each ticket, which is \( p = 10 \).

### Final Result

In terms of the format you requested:

- Let \( p = 10 \)
- Substituting it back, we can express it as \( 6(p - 1.50) = 51 \), which simplifies correctly as follows:

\[
6(10 - 1.50) = 51
\]
\[
6 \cdot 8.50 = 51
\]

So, Dez buys 6 tickets at a discounted price of \( 10 - 1.50 = 8.50 \) each for a total of $51.