SELLING PEANUTS-samuel operates a small peanut stand. He estimates that he can sell 600 bags of peanuts per day if he changes 50 cents for each bag. He determines that can sell 20 more bags for each 1 cent reduction in price.
A. What would his revenue be if he changed 48 cent per bag?
B. What should he charge in order to have receipts of $315?
Since revenue = quantity*price, after x 1-cent reductions, the revenue is
r(x) = (600+20x)(0.50-0.01x)
Now use that to answer the questions.
To answer these questions, we need to understand the relationship between the price, the number of bags sold, and the revenue.
Let's start by defining the variables:
P = Price per bag (in cents)
N = Number of bags sold per day
R = Revenue (in dollars)
According to the information given, Samuel estimates that he can sell 600 bags per day if he charges 50 cents for each bag. He also determines that he can sell 20 more bags for each 1 cent reduction in price. This means that for each 1 cent reduction in price, he can sell N + 20 more bags.
Now, let's calculate the number of bags sold for each price:
For P = 50 (original price), N = 600.
For P = 49 (1 cent reduction), N = 600 + 20 = 620.
For P = 48 (2 cents reduction), N = 620 + 20 = 640.
A. What would his revenue be if he charged 48 cents per bag?
To calculate the revenue, we need to multiply the number of bags sold by the price per bag and divide by 100 to convert it to dollars:
R = (N * P) / 100
R = (640 * 48) / 100
R = 307.20 dollars
The revenue would be $307.20 if he charged 48 cents per bag.
B. What should he charge in order to have receipts of $315?
To find the price he should charge, we need to rearrange the revenue formula:
P = (R * 100) / N
P = (315 * 100) / N
Since we don't know the number of bags sold (N) according to the given information, we can't determine the exact price he should charge to have receipts of $315.