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.
-
Expand the left side: \[ 6t - 9 = 51 \]
-
Add 9 to both sides: \[ 6t = 60 \]
-
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.
1 answer