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?

Rationale

y = 2(x + 1)

Liza's age can be expressed as twice Shawn's age, and since Shawn is one year older than Wendy, we can derive the equation by substituting Wendy's age into Liza's age expression. Therefore, Liza's age in terms of Wendy's age is accurately represented by the equation y = 2(x + 1).

A (y = x + 1) YOUR ANSWER

This equation suggests that Liza is only one year older than Wendy. However, according to the problem, Liza is twice as old as Shawn, and Shawn is one year older than Wendy, which does not support this equation.

B (y = 2x) YOUR ANSWER

This equation implies that Liza is twice as old as Wendy, which is not correct. The relationship established in the problem states that Liza is twice Shawn's age, and Shawn's age is one year greater than Wendy's, leading to a different relationship.

C (y = 2x + 1) YOUR ANSWER

While this equation might seem plausible, it incorrectly asserts that Liza is twice Wendy's age plus one additional year. Instead, Liza's age is derived from Shawn's age, which is one year more than Wendy's, thus invalidating this option.

D (y = 2(x + 1)) CORRECT

This equation accurately reflects the relationships described in the problem. Here, it shows that Liza's age (y) is twice the age of Wendy (x) plus one year, which accounts for Shawn being one year older than Wendy and correctly reflects the age relationships.

Conclusion

The correct equation representing the age relationships among Liza, Shawn, and Wendy is y = 2(x + 1). This formula accurately captures the essence of the problem, where Liza's age is directly linked to Shawn's age, who is one year older than Wendy. Understanding these relationships is essential for solving similar age-related problems in algebra.

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?

y = 2(x + 1)

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