Question

math - 8th grade

1. the table shows the amount of money a student has remaining after purchasing books at a book fair, where each book costs the same amount of money.

number of books purchased	remaining amount of money
2	$33.10
3	$18.15

according to the table, which statement is true?
a the cost of each book is $14.95 because the remaining amount of money decreases by $14.95 for each additional book purchased.
b the cost of each book is $15.00 because the remaining amount of money decreases by $15.00 for each additional book purchased.
c the cost of each book is $14.95 because the remaining amount of money decreases by $14.95 for each additional book purchased.
d the cost of each book is $15.00 because the remaining amount of money decreases by $15.00 for each additional book purchased.

Explanation:

Step1: Calculate the difference between the remaining amounts when the number of books purchased increases by 1.

First, find the difference between the remaining money when 2 books are purchased and 1 book is purchased: $\$38.10 - \$48.05 = -\$9.95$? Wait, no, wait, the first row: 1 book, remaining $\$48.05$; second row: 2 books, remaining $\$38.10$; third row: 3 books, remaining $\$28.15$. Wait, let's recalculate. From 1 to 2 books: $48.05 - 38.10 = 9.95$? Wait, no, the remaining money decreases, so the cost per book is the decrease in remaining money. So from 1 book to 2 books: remaining money goes from $\$48.05$ to $\$38.10$. The difference is $48.05 - 38.10 = 9.95$? Wait, no, wait the numbers: Wait, maybe I misread. Wait, 1 book: $\$48.05$ remaining; 2 books: $\$38.10$ remaining; 3 books: $\$28.15$ remaining. So the decrease from 1 to 2 books: $48.05 - 38.10 = 9.95$? Wait, but the options have $14.95$, $15.00$, etc. Wait, maybe I misread the table. Wait, maybe the first row is 1 book, remaining $\$48.05$; second row 2 books, remaining $\$38.10$? No, that would be a decrease of $9.95$, but the options don't have that. Wait, maybe the first row is 1 book, remaining $\$48.05$; second row 2 books, remaining $\$33.10$? Wait, the user's image: let's check again. The table: Number of Books Purchased: 1, Remaining Amount: $48.05; 2, $33.10; 3, $18.15. Ah! I misread the second row. So 1 book: $48.05; 2 books: $33.10; 3 books: $18.15. Now calculate the difference between 1 and 2: $48.05 - 33.10 = 14.95$. Then between 2 and 3: $33.10 - 18.15 = 14.95$. So the cost per book is $14.95, because the remaining money decreases by $14.95 for each additional book. So option C.

Step2: Verify the difference between each consecutive remaining amount.

For 1 to 2 books: $48.05 - 33.10 = 14.95$. For 2 to 3 books: $33.10 - 18.15 = 14.95$. So the decrease is consistent at $14.95 per book, which means the cost per book is $14.95. So option C is correct.

Answer:

C. The cost of each book is $14.95 because the remaining amount of money decreases by $14.95 for each additional book purchased.