29. Liza is twice as old as Shawn, and Shawn is one year older than Wendy. If Liza is y years old and Wendy is x years old, then which of the following equations is a true statement?
Answer: D
Liza's age can be expressed as twice the age of Shawn, who is one year older than Wendy.
The correct equation that represents the relationship between Liza, Shawn, and Wendy's ages is \(y = 2(x + 1)\), where \(y\) is Liza's age and \(x\) is Wendy's age.
A) y = x + 1
This equation suggests that Liza's age is only one year older than Wendy's age. However, based on the information given, Liza is twice as old as Shawn, who is one year older than Wendy, making this option incorrect.
B) y = 2x
This equation would imply that Liza's age is twice Wendy's age. However, since Shawn is one year older than Wendy and Liza is twice Shawn's age, this relationship does not hold, making this option incorrect.
C) y = 2x + 1
This equation suggests that Liza's age is twice Wendy's age plus one year. However, this does not accurately reflect the relationships provided in the question, as it does not account for Shawn being one year older than Wendy. Thus, this option is also incorrect.
D) y = 2(x + 1)
This equation correctly reflects the relationships described; it states that Liza's age is twice that of Shawn's age, which can be expressed as one year older than Wendy's age (x + 1). Therefore, this option is correct.
Conclusion
The correct equation, \(y = 2(x + 1)\), accurately captures the relationships between the ages of Liza, Shawn, and Wendy. All other options fail to represent this relationship correctly, either misrepresenting the ages or failing to consider the additional year that Shawn is older than Wendy.