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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?

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!

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

Katherine P.

really great. appreciate it!!

3/1/2013

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

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