Question

tickets are on sale for 1.50 off regular price dez buy six tickets and spends 51.00 write and solve equation for t tickets and form of p(x-q)=r

Answer 1

Let's denote:

- \( t \) as the regular price of one ticket.
- The discounted price for one ticket is \( t - 1.50 \).
- If Dez buys six tickets at the discounted price, the total cost can be expressed as \( 6(t - 1.50) \).

According to the problem, Dez spends a total of $51.00 on these six tickets. Therefore, we can write the following equation:

\[
6(t - 1.50) = 51
\]

Now, let's solve this equation step by step.

1. Expand the left side:
\[
6t - 9 = 51
\]

2. Add 9 to both sides:
\[
6t = 60
\]

3. Divide both sides by 6:
\[
t = 10
\]

Now we have found the regular price \( t \) to be $10.

Next, we can express the problem in the form \( p(x - q) = r \).

In this case, let's set:
- \( p = 6 \) (the number of tickets),
- \( x = t \) (the regular price of one ticket, which we found to be $10),
- \( q = 1.50 \) (the discount),
- \( r = 51 \) (the total amount spent).

Now we can rewrite the equation in the required form:

\[
6(t - 1.50) = 51
\]

So, the equation in the form \( p(x - q) = r \) is:

\[
6(t - 1.50) = 51
\]

Where:
- \( p = 6 \),
- \( x = t \),
- \( q = 1.50 \),
- \( r = 51 \).

This clearly defines the relationship and allows us to understand how the total cost of tickets relates to their price and the discount.