Question

Jay owns some DVDs. Lamar lives next to Jay and three houses from Freda. Lamar has 2 fewer DVDs than Jay. Davina lives on the other side of Jay and has three times as many DVD's as Lamar. Bart lives in house 2 and has 4 more DVD's than Jay. If Tara had 13 more DVD's, she would have four times as many as Jay. Jay acquired all of his DVD from freda, who lives in house 6. Freda had 17 DVD before she gave "p" of them to Jay. the person in house 5 owns the most DVD's wat is the value of p?​

Answer 1

6

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.

_____

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.