Let's analyze the problem step by step to determine how many tickets Stacy bought and which operations are involved.
- The original price of each ticket is $36.
- She received a $19 discount, which means the effective price per ticket is \( 36 - 19 = 17 \) dollars.
- The total amount she paid for the tickets is $53.
Let \( X \) represent the number of tickets she bought. The equation to represent the situation is:
\[ 17X = 53 \]
To solve for \( X \), we would need to perform division:
\[ X = \frac{53}{17} \]
Calculating that gives us \( X = 3.117... \). Since she cannot buy a fraction of a ticket, we should check our operations:
The correct setup should be:
\[ 36X - 19 = 53 \] Simplifying it gives: \[ 36X = 53 + 19 \] \[ 36X = 72 \] Now, dividing gives us:
\[ X = \frac{72}{36} = 2 \]
This shows that she bought 2 tickets.
Now, with respect to the operations involved in solving the equation,
- The equation started with multiplication (when you consider \( 36X \)).
- Then we adjusted by adding \( 19 \) to both sides, which involves addition.
- Finally, division is required to isolate \( X \).
The best match to the operations involved considering the main initial equation \( 36X - 19 = 53 \) is:
A. Subtraction and multiplication (since we used these in the original establishment of the ticket price).
However, the total calculation also involved addition to collect the total amount correctly in the middle of the solution process. Thus, if you're strictly following your question through the identified equation, it is subtraction and multiplication strictly because of the subtraction used in determining the price after discount, then further moves to isolate \( X \).
So considering the clear steps:
- Start with multiplication (36X)
- Subtract and add to isolate on both sides
- Finally, you would divide to solve.
The operations involved then are best summarized as subtraction and division when you isolate \( X \).
Thus the answer is B. Subtraction and division.
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