For $4.50 a grocer buys a case of fruit which contains 14 dozen. She knows that four dozen will spoil before she sells them. At what price per dozen must she sell the god ones to gain 1/3 of the whole cost?
The grocer must sell the good ones for $3.00 per dozen to gain 1/3 of the whole cost.
Well, it sounds like this grocer is in quite a pickle! But fear not, I, the hilarious Clown Bot, am here to help calculate the price per dozen.
First, let's break it down. The grocer purchases a case of fruit for $4.50, which contains 14 dozen. If four dozen are going to spoil, that leaves us with 10 good dozen.
To gain 1/3 of the whole cost, the grocer needs to make up for the cost of the entire case. So, if we divide the cost by the remaining good dozen, we can find the price per dozen.
$4.50 divided by 10 gives us $0.45. Therefore, the grocer must sell each good dozen for a price of $0.45 to gain 1/3 of the whole cost.
In conclusion, the grocer needs to make sure the price isn't too fruitful, but not too pricey either. Selling at $0.45 per dozen should help them achieve their goal!
To find out at what price per dozen the grocer must sell the good ones to gain 1/3 of the whole cost, we will follow these steps:
Step 1: Determine the total cost of the case of fruit.
Given that the grocer bought the case of fruit for $4.50 and it contains 14 dozen, we can calculate the total cost by dividing the price by the number of dozens:
Total cost = $4.50 / 14 = $0.3214 per dozen
Step 2: Calculate the cost of four dozens that will spoil.
Given that four dozens will spoil before the grocer sells them, we multiply the cost per dozen by four:
Cost of spoiled dozens = $0.3214/dozen * 4 = $1.2856
Step 3: Calculate the remaining cost after deducting the spoiled dozens.
To find the remaining cost after deducting the spoiled dozens, we subtract the cost of spoiled dozens from the total cost:
Remaining cost = Total cost - Cost of spoiled dozens
Remaining cost = $0.3214/dozen * (14 - 4) - $1.2856
Remaining cost = $0.3214/dozen * 10 - $1.2856
Remaining cost = $3.214 - $1.2856
Remaining cost = $1.9284
Step 4: Determine the selling price per dozen to gain 1/3 of the whole cost.
To find the selling price per dozen that allows the grocer to gain 1/3 of the whole cost, we multiply the remaining cost by 1/3 and then divide by the number of dozens:
Selling price per dozen = (Remaining cost * 1/3) / (10 - 4)
Selling price per dozen = ($1.9284 * 1/3) / 6
Selling price per dozen = $0.6428 / 6
Selling price per dozen ≈ $0.107
Therefore, the grocer must sell the good ones at approximately $0.107 per dozen to gain 1/3 of the whole cost.
To solve this problem, we need to determine how much the grocer paid for the case of fruit, and then calculate the selling price per dozen to gain 1/3 of the whole cost.
Let's break it down step by step:
1. Determine the cost of one dozen fruit.
The grocer bought a case of fruit for $4.50, which contains 14 dozen. So, to find the cost of one dozen, we divide the total cost by the number of dozen:
Cost of one dozen = Total cost / Number of dozen
Cost of one dozen = $4.50 / 14
2. Calculate the cost of four dozen that will spoil.
Since we know that four dozen will spoil, we can multiply the cost of one dozen by four to find the value:
Cost of four dozen = Cost of one dozen x 4
3. Calculate the cost of the "good" fruit.
To find the cost of the "good" fruit, subtract the cost of four dozen that will spoil from the total cost:
Cost of good fruit = Total cost - Cost of four dozen
4. Calculate the desired profit.
The grocer wants to gain 1/3 of the whole cost, so we can calculate this by multiplying the total cost by 1/3:
Desired profit = Total cost x (1/3)
5. Determine the selling price per dozen.
To find the selling price per dozen, divide the desired profit by the number of dozen:
Selling price per dozen = Desired profit / Number of dozen
By following these steps, we can calculate the selling price per dozen for the grocer.