neeraj.kaushal
Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy?
(1) The total cost of hardcover books that Juan bought was at least $150
(2) The total cost of all books that Juan bought was less than $260
We are given that Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each, and that he bought more than 10 paperback books. If we let p = the number of paperback books Juan bought and h = the number of hardcover books, the total cost of the paperback books is 8p, the total cost of the hardcover books is 25h, and the total cost of all books is 8p + 25h.
We need to determine the value of h, the number of hardcover books purchased by Juan.
Statement One Alone:
The total cost of the hardcover books that Juan bought was at least $150.
Using the information in statement one, we can create the following inequality:
25h ≥ 150
h ≥ 6
Thus, at least 6 hardcover books were purchased. However, we cannot determine the exact number of hardcover books purchased by Juan. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
The total cost of all the books that Juan bought was less than $260.
Using the information in statement two, we can create the following inequality:
8p + 25h ≤ 260
We still do not have enough information to determine how many hardcover books were purchased by Juan.
Statements One and Two Together:
From the given information as well as our two statements, we know that p > 10, h ≥ 6, and that 8p + 25h ≤ 260.
Since p > 10, Juan, at minimum, purchased 11 paperback books. If we use 11 for p in the inequality 8p + 25h ≤ 260, then we have:
88 + 25h ≤ 260
25h ≤ 172
h ≤ 6 22/25
Recall that h ≥ 6, and since h has to be a whole number, Juan must have purchased 6 hardcover books.
Answer: C