For $4.50 a grocer buys a case of fruit which contains 14 dozen. She knows that four dozen will spoil before sells them. At what price per dozen must she sell the good ones to gain 1/3 of the whole cost.
cost: 4.50*14
revenue after spoilage: 10p
we want
10p = 4/3 (4.50*14)
p = 8.40
To find the price per dozen at which the grocer must sell the good ones, let's break down the problem step by step:
Step 1: Calculate the total cost of the case of fruit.
The grocer buys the case of fruit for $4.50. Since there are 14 dozen in the case, we can calculate the cost per dozen by dividing the total cost by the total number of dozens:
Total cost = $4.50
Total dozens = 14 dozen
Cost per dozen = Total cost / Total dozens
Cost per dozen = $4.50 / 14 dozen
Step 2: Calculate the cost of the spoiled dozens.
The problem states that four dozen will spoil before selling. To find the cost of the spoiled dozens, we multiply the cost per dozen by the number of spoiled dozens:
Cost of spoiled dozens = Cost per dozen x Number of spoiled dozens
Cost of spoiled dozens = ($4.50 / 14 dozen) x 4 dozen
Step 3: Calculate the desired profit.
The problem mentions that the grocer wants to gain 1/3 of the whole cost. To calculate this profit, we multiply the total cost by 1/3:
Desired profit = Total cost x 1/3
Desired profit = $4.50 x 1/3
Step 4: Calculate the cost of the good dozens.
The cost of the good dozens is the total cost minus the cost of the spoiled dozens:
Cost of good dozens = Total cost - Cost of spoiled dozens
Cost of good dozens = $4.50 - ($4.50 / 14 dozen) x 4 dozen
Step 5: Calculate the price per dozen to gain the desired profit.
To calculate the price per dozen, we divide the cost of the good dozens by the number of dozens:
Price per dozen = Cost of good dozens / Number of good dozens
Price per dozen = ($4.50 - ($4.50 / 14 dozen) x 4 dozen) / (14 dozen - 4 dozen)
By simplifying and evaluating the above expression, you can find the price per dozen that the grocer must sell the good ones to gain 1/3 of the whole cost.
To solve this problem, we need to determine the total cost of the case of fruit, the cost of the spoiled fruit, and the selling price per dozen of the good fruit. Let's break it down step by step:
Step 1: Calculate the cost of the case of fruit.
The grocer buys the case of fruit for $4.50. Since there are 14 dozen in a case, we divide the total cost by the number of dozen: $4.50 / 14 = $0.3214 per dozen.
Step 2: Determine the cost of the spoiled fruit.
The problem states that four dozen will spoil before the grocer sells them. Therefore, we need to calculate the cost of those spoiled dozens. Each dozen costs $0.3214, so the cost of four dozen is 4 * $0.3214 = $1.2856.
Step 3: Calculate the remaining cost (good fruit cost).
To gain 1/3 of the whole cost, the grocer wants to recover 1/3 of the total cost, which includes the cost of the good fruit and the spoiled fruit. We already know the cost of the spoiled fruit ($1.2856). So, the remaining cost is (1 - 1/3) * $4.50 = $3.00.
Step 4: Find the selling price per dozen of the good fruit.
The remaining cost is the cost of the good fruit. Since there are 14 dozen in total and four dozen are spoiled, the grocer has 14 - 4 = 10 dozen of good fruit. To find the selling price per dozen, we divide the remaining cost by the number of dozen: $3.00 / 10 = $0.30 per dozen.
Therefore, the grocer must sell the good fruit for $0.30 per dozen in order to gain 1/3 of the whole cost.