Question

1. a bookstore offered mystery bags each containing 12 books. the quantity of each type of book was the same in each mystery bag. a shopper bought 3 mystery bags and found that 6 books were spy novels. based on this information, which prediction can the shopper make about buying mystery bags in the future? a. there will be 4 more spy novels in 8 bags than in 6 bags. b. there will be 2 more spy novels in 6 bags than in 4 bags. c. there will be 1 more spy novel in 9 bags than in 8 bags. d. there will be 6 more spy novels in 10 bags than in 8 bags.

Explanation:

Step1: Find the rate of spy novels per bag

First, we know that 3 bags have 6 spy novels. So the number of spy novels per bag is calculated by dividing the total number of spy novels by the number of bags. That is $\frac{6}{3} = 2$ spy novels per bag.

Step2: Analyze each option

• Option A: For 8 bags, the number of spy novels is $8\times2 = 16$. For 6 bags, it's $6\times2 = 12$. The difference is $16 - 12 = 4$. But let's check other options too.
• Option B: For 6 bags, spy novels are $6\times2 = 12$. For 4 bags, it's $4\times2 = 8$. The difference is $12 - 8 = 4$, not 2. So B is incorrect.
• Option C: For 9 bags, spy novels are $9\times2 = 18$. For 8 bags, it's $8\times2 = 16$. The difference is $18 - 16 = 2$, not 1. So C is incorrect.
• Option D: For 10 bags, spy novels are $10\times2 = 20$. For 8 bags, it's $8\times2 = 16$. The difference is $20 - 16 = 4$, not 6. So D is incorrect. Wait, but in Step 2 for Option A, we had a difference of 4. But let's re - check the calculation for Option B again. Wait, maybe I made a mistake. Wait, the rate is 2 spy novels per bag.

Wait, let's re - calculate Option B: 6 bags: $6\times2 = 12$; 4 bags: $4\times2 = 8$; $12 - 8 = 4$. Option A: 8 bags: $8\times2 = 16$; 6 bags: $6\times2 = 12$; $16 - 12 = 4$. Option B says 2 more, which is wrong. Option A says 4 more, which is correct. Wait, but let's check the problem again. Wait, maybe I miscalculated the rate. Wait, 3 bags have 6 spy novels, so per bag is 2. So for 8 bags: 16, 6 bags: 12, difference 4. So Option A is correct? But wait, let's check the original problem again. Wait, maybe I made a mistake in Option B. Wait, 6 bags: 62 = 12, 4 bags: 42 = 8, 12 - 8 = 4. So Option A has a difference of 4, Option B has 4, Option C has 2, Option D has 4. Wait, no, Option A says "4 more in 8 bags than in 6 bags", which is correct as 16 - 12 = 4. But let's check the options again. Wait, maybe I made a mistake in the initial rate. Wait, 3 bags, 6 spy novels. So per bag is 2. So:

• A: 8 bags: 16, 6 bags: 12, difference 4. Correct?
• B: 6 bags: 12, 4 bags: 8, difference 4. But option B says 2 more. So B is wrong.
• C: 9 bags: 18, 8 bags: 16, difference 2. Option C says 1 more. Wrong.
• D: 10 bags: 20, 8 bags: 16, difference 4. Option D says 6 more. Wrong.

So the correct option is A.

Answer:

A. There will be 4 more spy novels in 8 bags than in 6 bags.