One year ago, the cost, in dollars, of a laptop model was x. Today, the cost of the laptop model can be represented by the given expression. Which statements about the situation are true? An equivalent expression that represents this situation is x − 0.21x. The cost of the laptop model increased by 79%. An equivalent expression that represents this situation is x − 0.79x. An equivalent expression that represents this situation is x + 0.79x. The cost of the laptop model decreased by 21%. An equivalent expression that represents this situation is x + 0.21x.

1 answer

Let's analyze the statements one by one in relation to the given situation.

  1. An equivalent expression that represents this situation is x − 0.21x.

    • This is true. The expression \( x - 0.21x \) simplifies to \( 0.79x \), meaning the cost of the laptop is now 79% of its original cost, which indicates a decrease of 21%.
  2. The cost of the laptop model increased by 79%.

    • This is false. If the cost decreased by 21%, it means it did not increase by 79%; rather it decreased to 79% of its original cost.
  3. An equivalent expression that represents this situation is x − 0.79x.

    • This is false. The expression \( x - 0.79x \) simplifies to \( 0.21x \), which would suggest that the remaining cost is only 21% of the original, indicating a decrease — this does not correctly represent the situation where the cost is now 79% of the original.
  4. The cost of the laptop model decreased by 21%.

    • This is true. As established in the first statement, if the new cost corresponds to \( 0.79x \), that means it has decreased by 21%.
  5. An equivalent expression that represents this situation is x + 0.21x.

    • This is false. The expression \( x + 0.21x \) simplifies to \( 1.21x \), which indicates an increase in cost by 21%, contradicting the fact that the cost decreased.
  6. An equivalent expression that represents this situation is x + 0.79x.

    • This is false. The expression \( x + 0.79x \) simplifies to \( 1.79x \), suggesting a significant increase in cost rather than a decrease.

Summary of True Statements:

  • An equivalent expression that represents this situation is \( x - 0.21x \).
  • The cost of the laptop model decreased by 21%.

The rest of the statements are false given the context.