SOLUTION: Im having a lot of trouble on this problem and i really need some help if you have the time. Here is the problem. Missing proceeds. Ruth and Betty sell apples at a farmers market

Question 335738: Im having a lot of trouble on this problem and i really need some help if you have the time. Here is the problem.
Missing proceeds. Ruth and Betty sell apples at a farmers
market. Ruth�s apples sell at 2 for $1 while Betty�s slightly
smaller apples sell at 3 for $1. When Betty leaves to pick
up her kids they each have 30 apples and Ruth takes
charge of both businesses. To simplify things, Ruth puts all
60 of the apples together and sells them at 5 for $2. When
Betty returns, all of the apples have been sold, but they
begin arguing over how to divide up the proceeds. What
is the problem? Explain what went wrong.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since "Ruth�s apples sell at 2 for $1", this means that 2 apples = $1. Divide both sides by 2 to get 1 apple = 1/2 dollars

So one of Ruth's apples is 50 cents.

Because "Betty�s slightly smaller apples sell at 3 for $1", we know that 3 smaller apples = $1 and that 1 smaller apple = 33 cents (rounded to the nearest cent)

Now if all of the apples are sold in groups of 5 for $2, then 5 apples = $2 which means that 1 apple = 2/5 dollars or 1 apple = 40 cents.

Recall that the bigger apples sold at 50 cents a piece, while the smaller ones sold at about 33 cents a piece. So the 40 cent per apple price is too low for the larger apples and too high for the smaller apples. So there's either going to be more money or less money than expected when everything is sold.

What they're expecting:

There are 30 large apples. If each is sold at 50 cents, then 30(0.5) = 15 dollars is made.

There are 30 small apples. Selling them all (at 33 cents an apple) generates about 30(0.33)= 9.90 dollars

Add the two figures up to get 15+9.90 = 24.90

So they're expecting to make about $24.90

On the other hand...

What happens when the apples are sold at 5 for $2:

Every apple is now 40 cents a piece (see above). So selling all 60 apples brings in 60(0.40) = 24 dollars

So only $24 is made when selling apples at 5 for $2.

This means that they lost 90 cents. This may not seem like a big deal (it's not really), but imagine scaling up the amount of apples sold. If more apples are sold, then this difference will be bigger (ie If they sold 120 apples, they'd lose about $3.60, which is a bigger difference).

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