Answer:
6
Step-by-step explanation:
Freda lives in house 6. Lamar lives 3 houses from Freda, so lives in house 3. Jay lives next to Lamar, but not in house 2, which is Bart's. So, Jay lives in house 4 and Davina lives in house 5, on the other side of Jay from Lamar.
Davina lives in house 5, so has the most DVDs.
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Since Freda gave p DVDs to Jay, she has 17-p. Lamar has p-2, Bart has p+4, Tara has 4p-13, and Davina has the most at 3(p-2).
We want Davina to have the most DVDs, so there are some inequalities that must be true:
3(p-2) > 4p-13 ⇒ p < 7
3(p-2) > p +4 ⇒ p > 5
The only value of p satisfying both of these requirements is p = 6.
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Tara lives in house 1 and has 11 DVDs.
Bart lives in house 2 and has 10 DVDs.
Lamar lives in house 3 and has 4 DVDs.
Jay lives in house 4 and has 6 DVDs.
Davina lives in house 5 and has 12 DVDs. (the most)
Freda lives in house 6 and has 11 DVDs.
