SOLUTION: woman bought a number of items for $120. She realized that if she had bought 16 more items for the same money, she would have paid 24 less per item. How many items did she buy?

Question 1030615: woman bought a number of items for $120. She realized that if she had bought 16 more items for the same money, she would have paid 24 less per item. How many items did she buy?

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
First solution posting REMOVED and replaced with the discussion shown below:

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Check my email response to you. Explanation giving a better equation should be much more helpful there.

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This may be better, and more reliable:

Purchase of items is exchange of money in one direction and a number of items in the other direction. One can choose some numbers to symbolize the count of items, and the COST of money given for those items. Remember, COST is the amount of money paid.

PRICE is the ratio of cost to 1 item, meaning how much is to be paid for ONE item. Price can also be meant as ratio of money paid for any given quantity of an item.

Let me use these variables to help discuss.
n, a number of items bought or to be bought
p, the price of the item or a set quantity of the items
c, amount of money paid in purchasing some item

Think of the relationship among these as a kind of uniform rate. This can be .
This will look better on paper; I can only write in simple plain text in email.
Multiply both members by n and this makes:

This gives you a way to account for cost. Number of items multiplied by the price is the cost.
That is the fundamental concept which is used for thinking a pathway to solving the problem exercise which you posted.

"Sixteen more for the same 120 dollars..."
Quantity now n+16.
The cost still expected as given, $120.
Price is

That price is 24 dollars less PER ITEM.

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