To solve the problem using the equation \(36x - 19 = 53\), we can identify the operations needed:
- The term \(36x\) represents the total cost of the tickets.
- The $19 represents the discount that is subtracted from the total ticket price.
- The equation states that after applying the discount, the amount paid is $53.
To isolate \(x\), the operations involved are:
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First, you add 19 to both sides to eliminate the discount: \[ 36x = 53 + 19 \]
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Then, you divide both sides by 36 to solve for \(x\): \[ x = \frac{72}{36} \]
Thus, the operations needed to solve this problem are addition (to add the discount back) and division (to find the number of tickets).
So, the correct answer is:
addition and division