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A passenger bought a vase for $1,210 at 110% of its actual value. What was the actual value of the vase?

  1. $1,000

  2. $1,100

  3. $1,150

  4. $1,200

The correct answer is: $1,100

To determine the actual value of the vase, it's important to understand the relationship between the purchased price and the percentage at which it was bought. The passenger bought the vase at 110% of its actual value. This means that the paid amount of $1,210 represents 110% of what the vase is truly worth. To find the actual value, you can set up the equation where the actual value is represented as "X." According to the problem, we have: \[ 1.10X = 1210 \] To isolate "X," divide both sides of the equation by 1.10: \[ X = \frac{1210}{1.10} \] \[ X = 1100 \] Therefore, the actual value of the vase is $1,100, which corresponds to the correct answer choice. It effectively converts the marked-up price back into the vase's true value based on the given percentage. The other options do not accurately reflect this calculation based on the percentage given, as they do not align with the derived actual value from the equation.