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.