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Jack has some magnets. He gives Kevin half his magnets plus 1 magnet
and gives bob half of his remaining magnets plus 2 magnets.
If Jack has 6 magnets left how many did he have at first.
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I will write a table showing each Jack's step separately.
1) Jack gives Kevin half his magnets.
2) Jack gives Kevin 1 additional magnet.
3) Jack gives Bob half remaining magnets.
4) Jack gives Bob 2 additional magnet.
5) At the end Jack has 6 magnets left.
Now move backward, from the end to the beginning.
From the table, you conclude that immediately before step 4 Jack had 6+2 = 8 magnets.
Hence, immediately before step 3) Jack had 8*2 = 16 magnets.
Hence, immediately before step 2) Jack had 16+1 = 17 magnets.
Hence, before step 1) Jack had 2*17 = 34 magnets.
Thus the problem is just solved, and the answer is
+------------------------------------+
| At first, Jack had 34 magnets. |
+------------------------------------+
Solved.
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Thus, I solved the problem MENTALLY.
The method, which I used, is called the BACKWARD METHOD.
Good for young student to wake up their minds and make them smile.
Also good for all other ages readers - for the same purpose.