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 good ones to gain 1/3 of the whole cost?
The price per dozen must be $2.17 in order to gain 1/3 of the whole cost.
Well, well, well, it looks like the grocer is in a bit of a pickle! Let me crunch some numbers and make a joke or two along the way for some berry-tasty fun!
Okay, let's start by finding the total cost of the case of fruit. The grocer bought it for $4.50, and since there are 14 dozen in the case, she paid 4.50/14 per dozen.
Now, let's calculate the cost of the four dozen that will spoil. Since there are four dozen in total, the grocer paid 4.50/14 * 4 for them.
To find out how much the good ones should be sold for, we need to figure out what 1/3 of the total cost is. We can then divide that amount by the remaining number of good dozens, 10.
Let's do the math:
Total cost per dozen: 4.50/14
Cost of spoiled dozens: 4.50/14 * 4
Remaining good dozens: 10
1/3 of the total cost: (4.50/14 * 14) / 3
Now, divide 1/3 of the total cost by the number of good dozens to find the price per dozen the grocer must sell them for.
And voilà, you've got your answer! I hope my numerical circus act brought a smile to your face. If not, I guess I'll have to say, "Orange you glad I tried?"
To find the price per dozen that the grocer must sell the good ones to gain 1/3 of the whole cost, we need to first determine the total cost of the case of fruit and then calculate the desired profit.
1. The case of fruit contains 14 dozen.
2. The grocer knows that four dozen will spoil, so she is left with 14 - 4 = 10 dozen good ones.
3. The total cost of the case of fruit is $4.50.
4. To gain 1/3 of the whole cost, the grocer wants to make a profit of 1/3 * $4.50 = $1.50.
5. The grocer wants to make this profit by selling the 10 dozen good ones.
6. To determine the price per dozen, we divide the desired profit by the number of dozen sold: $1.50 / 10 dozen = $0.15 per dozen.
Therefore, the grocer must sell the good ones for $0.15 per dozen in order to gain 1/3 of the whole cost.
To find the price per dozen at which the grocer must sell the good ones in order to gain 1/3 of the whole cost, we need to break down the problem step by step.
Step 1: Find the total cost of the case of fruit.
The grocer buys the case of fruit for $4.50.
Step 2: Find out how many dozens of fruit the grocer has.
The case contains 14 dozen.
Step 3: Determine how many dozens will spoil.
The problem states that 4 dozen will spoil. Therefore, the grocer will have 14 - 4 = 10 good dozens of fruit.
Step 4: Calculate the cost of each dozen.
To find the cost of each dozen, divide the total cost by the number of good dozens.
Cost of each dozen = Total cost / Number of good dozens
Cost of each dozen = $4.50 / 10 = $0.45
Step 5: Determine the desired profit.
The grocer wants to gain 1/3 of the whole cost. To calculate the desired profit, multiply the total cost by 1/3.
Desired profit = Total cost x 1/3
Desired profit = $4.50 x 1/3 = $1.50
Step 6: Calculate the selling price per dozen.
To find the selling price per dozen, add the desired profit to the cost of each dozen.
Selling price per dozen = Cost of each dozen + Desired profit
Selling price per dozen = $0.45 + $1.50 = $1.95
Therefore, the grocer must sell the good ones at a price of $1.95 per dozen in order to gain 1/3 of the whole cost.