For $1.80 a grocer buys a case of fruit which contains 12 dozen. She knows that tow 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 $1.80, is (1.8+0.6) dollars. The cost given was for all 12 dozen. NOW, the selling cost, or the revenue must be 2.40 dollars. This 2.40 dollars must be equally distributed among the 10 dozen which are still good.
2.40 dollars per 10 dozen is:
2.40/10=0.24 dollars per dozen.
This is 24 cents per dozen.
To find the price per dozen that the grocer must sell the good ones, we need to determine the total cost of the case of fruit and the cost of the spoiled fruit.
First, let's calculate the cost of the whole case of fruit:
12 dozen = 12 x 12 = 144 individual fruit
If the grocer buys the case for $1.80, the cost per individual fruit is $1.80 / 144 = $0.0125.
Next, let's calculate the cost of the spoiled fruit:
2 dozen = 2 x 12 = 24 individual fruit
The cost of the spoiled fruit is 24 x $0.0125 = $0.30.
Now, let's determine how much the grocer wants to gain from selling the good ones. We know that she wants to gain 1/3 of the whole cost.
1/3 x $1.80 = $0.60
To find the price per dozen for the good ones, let's subtract the cost of the spoiled fruit and the desired gain from the total cost:
$1.80 - $0.30 - $0.60 = $0.90
Finally, let's find the price per dozen by dividing the price for the good ones by the number of dozens:
$0.90 / 10 dozen = $0.09 per dozen
Therefore, the grocer must sell the good ones at a price of $0.09 per dozen to gain 1/3 of the whole cost.
To determine the price at which the grocer must sell the good dozens of fruit in order to gain 1/3 of the whole cost, we need to first calculate the total cost of the case of fruit.
The grocer bought the case for $1.80, and the case contains 12 dozen, so the cost of each dozen is $1.80 divided by 12, which equals $0.15.
Next, we need to find out how many dozens will be sold. The case contains 12 dozen, and two dozen are known to spoil, so the number of dozens that will be sold is 12 dozen minus 2 dozen, which equals 10 dozen.
Now, let's calculate the desired profit. The grocer wants to gain 1/3 of the whole cost, which is 1/3 multiplied by $1.80, which equals $0.60.
To find the selling price per dozen, we divide the desired profit by the number of dozens that will be sold. So, $0.60 divided by 10 dozen equals $0.06 per dozen.
Therefore, the grocer must sell the good dozens of fruit for $0.06 per dozen in order to gain 1/3 of the whole cost.
(1/3) * $1.80 = $0.60. = Income.
P = $0.60 / (12-2) = $0.06 / doz.