For their twentieth wedding anniversary, Richard and Sylvia had a party for several of their best friends. Things were going along just fine until one of their friends asked the happy couple who was older! Here's what they had to say. Richard: "I am older than my wife." Sylvia: "I am younger than my husband." That might have been the end of it, but one of the guests knew that at least one member of the couple was lying. Well, who is older, Richard or Sylvia?

Richard is older

Step-by-step explanation:

We can set up an inequality for both statements.

Let r equal Richard's age and s equal Sylvia's age.

"I am older than my wife."

Since Richard is speaking, the inequality would look like this:

r > s

This means Richard is older than Sylvia.

"I am younger than my husband."

Since Sylvia is speaking, the inequality would look like this:

s < r

This means that Sylvia is younger than Richard.

We can flip one inequality to "see" them from the same perspective.

Let's use s < r

To make it so that we can see the relationship from Richard's perspective, flip the entire inequality.

s < r

to

r > s

The inequality from the first quote is identical to this one!

Therefore, Richard is older than Sylvia.