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.
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)
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.