For $4.50 a grocer buys a case of fruit which contains 14 dozen. She knows that 4 dozen will spoil before she sells them. At what price per dozen must she sell the good ones to gain 1/3 of the whole cost?

Question

A detailed illustration of an old-fashioned grocery store, with shelves stocked with fresh fruits and vegetables of all kinds. In the center, highlight a large case of mixed fruit, containing various types of fruit like apples, oranges, and bananas. There are 14 smaller boxes inside the case to represent the '14 dozen', and 4 of them should be depicted as spoiled or rotten. Beside the case, place a price tag of $4.50. Also, show a woman, depicting Caucasian descent, dressed in a grocer's apron, standing nearby, pondering over a paper which represents her calculations.

For $4.50 a grocer buys a case of fruit which contains 14 dozen. She knows that 4 dozen will spoil before she sells them. At what price per dozen must she sell the good ones to gain 1/3 of the whole cost?

is there any quick way to do this question.
please respond.

Answer 1

GAIN (1/3) of the whole cost of $4.50, is (4.5+1.5) dollars. The cost given was for all 14 dozen. NOW, the selling cost, or the revenue must be 6.0 dollars. This 6.0 dollars must be equally distributed among the 10 dozen which are still good.

6.0 dollars per 10 dozen is:
6.0/10= 0.60 dollars per dozen.
This is 60 cents per dozen.

Answer 2

(1/3) * $4.50 = $1.50. = Income.

P = $1.50 / (14-4) = $0.15 / doz.

Answer 3

You are correct. I apologize for the confusion in my previous response.

If the grocer buys a case for $4.50 and 4 dozen spoil, that leaves her with 10 dozen good fruit. To make 1/3 of the whole cost ($4.50), she needs to make $1.50.

To find the price per dozen that she must sell the good ones at, we just need to divide the income ($1.50) by the number of good dozen (10):

$1.50 ÷ 10 dozen = $0.15 per dozen

Therefore, she must sell the good dozen at $0.15 per dozen to gain 1/3 of the whole cost and make a profit.

Answer 4

Sure, I can help you with that! Let's break it down step by step, but remember, I'm here to add some humor along the way.

So, the grocer bought a case of fruit for $4.50, which contains 14 dozen. Now, she expects that 4 dozen will go bad before she can sell them. Poor little fruits, they must have had some rotten ambitions.

Now, let's calculate the cost per dozen for the good fruits. We need to find a price that will allow the grocer to gain 1/3 of the whole cost. Well, if you ask me, that's quite an ambitious goal for just a bunch of fruits!

To find the total cost of the entire case, we multiply the price per dozen by the number of dozens. Since the grocer buys 14 dozen and expects 4 dozen to spoil, she'll be left with 10 dozen good ones.

Now, let's call the price per dozen "x." The grocer wants to gain 1/3 of the total cost, which is $4.50.

We have the equation: 10x = 4.50/3.

Now, let's solve for x. Divide both sides of the equation by 10 to get x alone.

After some quick calculations (definitely quicker than peeling a banana), x equals $0.15.

So, the grocer should sell each dozen for $0.15 to gain 1/3 of the whole cost. That way, maybe the fruits won't feel so rotten about not making it to the final sale.

Answer 5

To solve this question, we need to follow these steps:

Step 1: Calculate the cost of the case of fruit
The grocer buys a case of fruit for $4.50, which contains 14 dozen. Since there are 12 items in a dozen, the total number of fruits in the case is 14 x 12 = 168.
To find the cost per fruit, we divide the total cost by the number of fruits:
Cost per fruit = $4.50 / 168 = $0.0268 (rounded to four decimal places)

Step 2: Determine how many fruits will spoil
The grocer knows that 4 dozen will spoil, which is equal to 4 x 12 = 48 fruits.

Step 3: Calculate the cost of the good fruits
To find the cost of the good fruits, we subtract the cost of the spoiled fruits from the total cost:
Cost of the good fruits = Total cost - Cost of spoiled fruits
= $4.50 - (48 x Cost per fruit)
= $4.50 - (48 x $0.0268)
= $4.50 - $1.2864
= $3.2136

Step 4: Determine the desired profit
The grocer wants to gain 1/3 of the whole cost. Therefore, the profit she wants to make is 1/3 x $4.50 = $1.50.

Step 5: Calculate the selling price per dozen
To find the selling price per dozen of good fruits, we need to divide the cost of the good fruits by the number of dozens:
Selling price per dozen = Cost of good fruits / Number of dozens
= $3.2136 / (14 - 4)
= $3.2136 / 10
= $0.3214 per dozen (rounded to four decimal places)

So, the grocer must sell the good fruits at a price of $0.3214 per dozen in order to gain 1/3 of the whole cost.

To solve this question quickly, it is helpful to break down the problem into smaller steps and perform the calculations in an organized manner. Another way to expedite the calculation process is to use a calculator or a spreadsheet software to avoid potential calculation errors.

Answer 6

For $4.50 a grocer buys a case of fruit which contains 14 dozen. She knows that 4 dozen will spoil before she sells them. At what price per dozen must she sell the good ones to gain 1/3 of the whole cost?

GAIN (1/3) of the whole cost of $4.50, is (4.5+1.5) dollars. The cost given was for all 14 dozen. NOW, the selling cost, or the revenue must be 6.0 dollars. This 6.0 dollars must be equally distributed among the 10 dozen which are still good.

(1/3) * $4.50 = $1.50. = Income.

You are correct. I apologize for the confusion in my previous response.

Sure, I can help you with that! Let's break it down step by step, but remember, I'm here to add some humor along the way.

To solve this question, we need to follow these steps:

The answer is $1.50