Problem Analysis:
The problem involves
deductive reasoning and requires us to analyze the given statements and rules to determine how many candles can be made from a box of 12 candles. Let's break it down step by step.
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Given Information:
1.
Candle Recycling Rule:
- Every time you burn a candle, you get a stub.
- Three stubs can be recycled into one new candle.
2.
Initial Setup:
- You start with a box of 12 candles.
3.
Objective:
- Determine how many total candles (including the original ones and those made from recycling) can be burned.
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Step-by-Step Solution:
####
Step 1: Initial Candles
You start with 12 candles. When you burn these 12 candles, you will have:
-
12 stubs (one stub per candle).
####
Step 2: First Recycling
With 12 stubs, you can recycle them into:
-
4 new candles (since 12 stubs ÷ 3 stubs/candle = 4 candles).
After burning these 4 new candles, you will have:
-
4 more stubs (one stub per candle).
####
Step 3: Second Recycling
Now you have the 4 stubs from the second set of candles. Recycle these 4 stubs:
- You can make
1 new candle (since 4 stubs ÷ 3 stubs/candle = 1 candle with 1 stub remaining).
After burning this 1 new candle, you will have:
-
1 more stub (from the candle you just burned).
####
Step 4: Third Recycling
At this point, you have:
- 1 stub from the last candle burned.
- 1 stub remaining from the previous recycling step.
This gives you a total of:
-
2 stubs.
Since you need 3 stubs to make a new candle, you cannot make another candle at this stage. However, you can save these 2 stubs for future use if more candles are burned later.
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Total Candles Burned:
Let's count all the candles that were burned:
1. The original 12 candles.
2. The 4 candles made from the first recycling.
3. The 1 candle made from the second recycling.
Adding these up:
- Total candles burned = 12 + 4 + 1 =
17 candles.
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Final Answer:
The total number of candles that can be burned from a box of 12 candles, including those made from recycling, is:
$$
\boxed{17}
$$
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Explanation:
The key to solving this problem is understanding the recycling process and keeping track of the stubs generated after each set of candles is burned. Each time you burn a set of candles, you generate stubs that can be used to make new candles, but you always need 3 stubs to create one new candle. This iterative process continues until you no longer have enough stubs to make a new candle. In this case, the process stops after the third recycling step because you are left with only 2 stubs, which is not enough to make another candle.
Parent Tip: Review the logic above to help your child master the concept of inductive deductive reasoning worksheet.
