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Sagot :
164
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We have two crucial pieces of information:
1. If you transfer 100 pebbles from pile A to pile B, the number of pebbles in pile B becomes twice the number of pebbles in pile A.
This can be written as the following equation:
- B + 100 = 2(A - 100) ⇒ B + 100 = 2A - 200 ⇒ B = 2A - 300
2. If you transfer 1 pebble from pile B to pile A, the number of pebbles in pile A becomes six times the number of pebbles in pile B.
This can be written as the following equation:
- A + 1 = 6(B - 1) ⇒ A + 1 = 6B - 6 ⇒ A = 6B - 7
We can substitute the value of B from equation 1 into equation 2:
- A = 6(2A - 300) - 7
- A = 12A - 1800 - 7
- A = 12A - 1807
- 1807 = 11A
- A = 1807/11
- A = 164 (rounded)
Therefore, pile A has at least 164 pebbles.
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