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A shop sells 1 chocolate at $1. you can exchange 3 wrappers for 1 chocolate. if you have $15, how many chocolates can you get?

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2 Answers

The key to problems like these are to:

  1. Identify the elements: dollars, wrappers, chocolates
  2. Identify (and remember!) the goal: changing dollars and wrappers into chocolates

You can write each element in terms of your goal (chocolate).

  • dollars ($1 = 1 chocolate)
  • sets of wrappers (3 wrappers = 1 chocolate)

Now work on the goal - change those dollars and wrappers into chocolate. After each calculation you make, check your balance - how many dollars and how many wrappers are left?

Balance: 15 dollars, 0 wrappers, 0 chocolates

  • Change dollars into chocolate and wrappers
  • Spend 15 dollars, Get 15 chocolates, 15 wrappers

New balance: 0 dollars, 15 wrappers, 15 chocolates

  • Change wrappers into chocolates and wrappers
  • Spend 15 wrappers, Get 5 chocolates and 5 wrappers

New balance: 0 dollars, 5 wrappers, 20 chocolates

  • Change wrappers into chocolates and wrappers
  • Spend 3 wrappers, Get 1 chocolate and 1 wrapper

New balance: 0 dollars, 3 wrappers, 21 chocolates

  • Change wrappers into chocolates and wrappers
  • Spend 3 wrappers, Get 1 chocolate and 1 wrapper

New balance: 0 dollars, 1 wrappers, 22 chocolates

Can you buy any more chocolates? Not with 0 dollars and less than 3 wrappers, so you know you're done!

Final Answer: 22 chocolates

If you found this explanation helpful, please click the "vote up" thumbs up button. :)

Katherine P.

 

Comments

Everything is okay.

But finally u will be left with 22 chocolates and 0 wrappers

From $15 -> 15 Chocolates and 15 Wrappers
From 15 Wrappers -> 5 Chocolates and 5 Wrappers
From 5 Wrappers -> 1 Chocolate,1 New Wrapper and 2 old Wrapper from previous balance
From 3 Wrappers -> 1 Chocolate, 0 Wrappers left

Final answer is 22 and no more wrappers left.
 
Curious... i percieve a major flaw in your answer. The joke is written in present tense. Thay being said, that means you walk up to a store with $15, you can only purchase 15 chocolates, I mean presumptively you would consume the chocolates, exchange, consume, and exchange... but the joke doesn't mention anything about leaving the store, but it says currently you have $15 and.... 
that being said, it would just depend, perceptionally, how one would Interpret the question. 
The answer is actualy 21 chocolates and you will have 2 wrapers left over.  
 
$15 = 15 chocolates
15 wrapers = 5 chocolates
3 wrapers = 1 chocolate 
2 wrapers left

$1 buys 1 Chocolate, so $15 buys 15 Chocolates.

15 Chocolates provides 15 wrappers, but it takes 3 wrappers to buy 1 chocolate.

15/3 = 5 chocolates you can buy from your original 15 chocolates

Now you have 5 new wrappers 

5/3 = 1.66, so you can buy 1 more chocolate.

So lets add it all up.

15 chocolates + 5 chocolates + 1 chocolate = 21 chocolates from your original $15