Chapter 5 - Relationships Within Triangles - 5-5 Indirect Proof - Practice and Problem-Solving Exercises - Page 320: 12

Statements II and III contradict each other.

If Val spent $34$ dollars for both items, at least one of the items has to cost more than $15$ dollars. If neither item costs more than $15$ dollars, then the two items will add up to less than $30$ dollars; therefore, statements II and III contradict each other.