SOLUTION: a grocer bought some oranges at a cost of 8 for 96 cents and then 2/3 times as many at a cost of 6 for 1.02. In order to make a profit 50%, he must sell all of them at a price of a

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Question 1196789: a grocer bought some oranges at a cost of 8 for 96 cents and then 2/3 times as many at a cost of 6 for 1.02. In order to make a profit 50%, he must sell all of them at a price of a dozen for $m. Find the value of m in dollars.
Found 3 solutions by greenestamps, josgarithmetic, MathTherapy:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The first batch cost him 96/8 = 12 cents each; the second batch cost him 102/6 = 17 cents each.

Using the fact that the number in the second batch was 2/3 the number in the first...
let 3x = # in first batch
then 2x = # in second batch

The total cost to him in cents was



The average cost to him for each orange was then that total cost, divided by the total number of oranges:



The oranges cost him, on average 14 cents each; to make a profit of 50%, he needs to sell them at 21 cents each, which means 12(21) = 252 cents or $2.52 per dozen.

ANSWER (price per dozen in dollars): 2.52
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
PRICE              QUANTITY          COST

8 for 96c           (3/2)n          (0.96/8)(3/2)n

6 for 102c           n               (1.02/6)n

The cost for the first two purchases



---------------dollars total the two first purchases

Quantity bought, first two purchases

----------------- how many each bought, first two purchases

PRICE EACH first two purchases


----------THE EFFECTIVE PRICE EACH in the two first purchases

You could find the value for on the way toward answering the question, about selling those to get 50% profit.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

a grocer bought some oranges at a cost of 8 for 96 cents and then 2/3 times as many at a cost of 6 for 1.02. In order to make a profit 50%, he must sell all of them at a price of a dozen for $m. Find the value of m in dollars.
Let N be the number of oranges purchased 1st
Then amount paid for the 1st purchase = 
With  being the amount purchased after, the amount paid for the 2nd purchase = 

With sale price of $m per dozen, each orange was sold for 

    Total number of oranges purchased: 

Total cost of  oranges: 

To realize a 50% profit, we then get:

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