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

1 answer

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.