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.
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)
1 answer