Question

part 1 of 2
think about the process there are 4,000 books in the town’s library. of these, 3,200 are fiction. to find the percent of the books that are fiction, first set up the percent equation.
setup the percent equation. choose the correct answer below
a. 3,200 = m · 4,000
b. 4,000 = m · 3,200
c. 4,000 = m · 3,200
d. 3,200 = m · 4,000

Explanation:

Step1: Recall Percent Equation

The percent equation is \( \text{Part} = \text{Whole} \times \text{Percent (in decimal)} \). Here, the whole number of books is 4,000 (Whole), the part (fiction books) is 3,200, and \( m \) is the percent (in decimal). So the equation should be \( 3200 = 4000 \times m \), which can be rewritten as \( 4000 = m \times 3200 \)? Wait, no. Wait, let's re-express. Wait, the formula is \( \text{Part} = \text{Whole} \times \text{Rate} \). So Part is 3200, Whole is 4000, Rate is \( m \) (decimal percent). So \( 3200 = 4000 \times m \), which is equivalent to \( 4000 \times m = 3200 \), or rearranged as \( 4000 = \frac{3200}{m} \)? No, wait the options: Let's check the options. Option C is \( 4000 = m \times 3200 \)? No, wait option D: \( 3200 = m \times 4000 \). Wait, let's parse the problem again. The problem says "setup the percent equation". The total books (whole) is 4000, the part (fiction) is 3200. The percent equation is \( \text{Part} = \text{Whole} \times \text{Percent} \) (where percent is in decimal, so \( m \) is the decimal percent). So \( 3200 = 4000 \times m \), which is option D? Wait no, let's check the options:

A. \( 3200 = m \times 4000 \) → same as \( 3200 = 4000m \)

B. \( 4000 = m \times 3200 \) → \( 4000 = 3200m \)

C. \( 4000 = m \times 3200 \) → same as B? Wait no, maybe typo. Wait the user's image: Let's re-express the options:

A. \( 3,200 = m \times 4,000 \)

B. \( 4,000 = m \times 3,200 \)

C. \( 4,000 = m \times 3,200 \) (maybe duplicate, but likely a typo, but let's check the problem. The correct percent equation is \( \text{Part} = \text{Whole} \times \text{Percent} \). So Part (3200) = Whole (4000) × Percent (m, decimal). So \( 3200 = 4000 \times m \), which is option A? Wait no, option A is \( 3200 = m \times 4000 \), which is the same as \( 3200 = 4000m \), which is correct. Wait, maybe I mixed up. Wait, the percent equation is \( \text{Part} = \text{Whole} \times \text{Rate} \), where Rate is the percent (decimal). So here, Part is 3200, Whole is 4000, Rate is \( m \). So \( 3200 = 4000 \times m \), which is option A? Wait no, the options:

Wait the user's image:

A. \( 3,200 = m \times 4,000 \)

B. \( 4,000 = m \times 3,200 \)

C. \( 4,000 = m \times 3,200 \) (maybe same as B)

D. \( 3,200 = m \times 4,000 \) (same as A? No, maybe typo. Wait, perhaps the correct equation is \( \text{Part} = \text{Whole} \times \text{Percent} \), so \( 3200 = 4000 \times m \), which is option A (or D, if D is \( 3200 = m \times 4000 \)). Wait, looking at the options, A and D: Let me check the original image again. The user's image:

Options:

A. \( 3,200 = m \cdot 4,000 \)

B. \( 4,000 = m \cdot 3,200 \)

C. \( 4,000 = m \cdot 3,200 \) (maybe duplicate)

D. \( 3,200 = m \cdot 4,000 \) (same as A? No, maybe a typo, but likely A and D are same, but perhaps the correct one is \( 3200 = 4000m \), which is option A (or D). Wait, maybe the correct answer is D? Wait no, let's think again. The percent equation is \( \text{Part} = \text{Whole} \times \text{Rate} \). So Part (3200) = Whole (4000) × Rate (m). So \( 3200 = 4000 \times m \), which is option A (or D, if D is written as \( 3200 = m \times 4000 \)). So the correct option is D? Wait no, A and D are same? Wait the user's image: Let me re-express the options as per the image:

A. \( 3,200 = m \times 4,000 \)

B. \( 4,000 = m \times 3,200 \)

C. \( 4,000 = m \times 3,200 \) (maybe a repeat)

D. \( 3,200 = m \times 4,000 \) (same as A? No, maybe a typo, but perhaps the intended correct is \( 3200 = 4000m \), which is option D? Wait no, A and D are same. Wait, maybe the correct answer is D? Wait, no, let's check the problem again. The total books are 4000 (whole), fiction is 3200 (part). The percent equation is \( \text{Part} = \text{Whole} \times \text{Percent} \), so \( 3200 = 4000 \times m \), which is option D (since D is \( 3,200 = m \times 4,000 \)). So the correct answer is D.

Answer:

D. \( 3,200 = m \cdot 4,000 \)