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n=1.273-4p The equation above was used...

`n=1.273-4p`
The equation above was used by the cafeteria in a large public high school to model the relationship between the number of slices of pizza, n, sold daily and the price of a slice of pizza, p in dollars. What does the number 4 represents in this equation?

A

For every $4 the price of pizza decrease, the caferia sells 1 more slice of pizza.

B

For every dollar the price of pizza decrease, the caferia sells 4 more slice of pizza.

C

For every $4 the price of pizza increase, the caferia sells 1 more slice of pizza.

D

For every dollar the price of pizza increase, the caferia sells 4 more slice of pizza.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the equation \( n = 1.273 - 4p \) and determine what the number 4 represents, we can follow these steps: ### Step 1: Understand the Variables The equation models the relationship between: - \( n \): the number of slices of pizza sold daily - \( p \): the price of a slice of pizza in dollars ### Step 2: Substitute Values for \( p \) To understand the effect of changing the price \( p \) on the number of slices sold \( n \), we can substitute different values for \( p \). 1. **Assume \( p = 4 \) (price is $4 per slice)**: \[ n = 1.273 - 4(4) = 1.273 - 16 = 1.257 \] So, when the price is $4, the cafeteria sells 1,257 slices of pizza. 2. **Assume \( p = 3 \) (price is $3 per slice)**: \[ n = 1.273 - 4(3) = 1.273 - 12 = 1.261 \] So, when the price is $3, the cafeteria sells 1,261 slices of pizza. 3. **Assume \( p = 2 \) (price is $2 per slice)**: \[ n = 1.273 - 4(2) = 1.273 - 8 = 1.265 \] So, when the price is $2, the cafeteria sells 1,265 slices of pizza. ### Step 3: Analyze the Changes Now, let's analyze the changes in the number of slices sold when the price decreases by $1: - From \( p = 4 \) to \( p = 3 \): \[ n \text{ changes from } 1,257 \text{ to } 1,261 \quad (\text{increase of } 4) \] - From \( p = 3 \) to \( p = 2 \): \[ n \text{ changes from } 1,261 \text{ to } 1,265 \quad (\text{increase of } 4) \] ### Step 4: Conclusion From the analysis, we can conclude that for every $1 decrease in the price of a slice of pizza, the number of slices sold increases by 4. Therefore, the number 4 in the equation represents the increase in the number of pizza slices sold for each $1 decrease in price. ### Final Answer The number 4 represents the increase in the number of pizza slices sold for every $1 decrease in the price of a slice of pizza. ---
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