Amelie is shopping for children’s books and puzzle books. She wants to purchase at least 2 more children’s books than puzzle books, but she can afford no more than 15 items total.

Question

If x represents the number of children’s books and y represents the number of puzzle books Amelie purchases, which point lies in the solution set?

A.
(4,12)
B.
(6,8)
C.
(12,4)
D.
(9,5)

Answer 1

To determine which point lies in the solution set, we need to consider the given conditions:

1) Amelie wants to purchase at least 2 more children's books than puzzle books.
2) She can afford no more than 15 items in total.

Let's check each option:

A) (4,12)
If Amelie purchases 4 children's books (x) and 12 puzzle books (y), she bought a total of 16 items. This exceeds the maximum of 15 items. Therefore, (4,12) is not in the solution set.

B) (6,8)
If Amelie purchases 6 children's books (x) and 8 puzzle books (y), she bought a total of 14 items. This is within the maximum of 15 items. Also, 6 is indeed 2 more than 8. Therefore, (6,8) lies in the solution set.

C) (12,4)
If Amelie purchases 12 children's books (x) and 4 puzzle books (y), she bought a total of 16 items. This exceeds the maximum of 15 items. Therefore, (12,4) is not in the solution set.

D) (9,5)
If Amelie purchases 9 children's books (x) and 5 puzzle books (y), she bought a total of 14 items. This is within the maximum of 15 items. Also, 9 is indeed 2 more than 5. Therefore, (9,5) lies in the solution set.

In conclusion, the points that lie in the solution set are:

B) (6,8)
D) (9,5)

Therefore, the correct answer is either B or D.