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There are 2 piles of gravel A and B. If you transfer 100 pebbles from pile A to pile B, the number of gravel in pile B is twice as many gravel in pile A. If you transfer 1 number of pebbles from pile B to pile A, the number of gravels in pile A is 6 times more than the number of gravel in pile B. Ask how many pebbles pile A has at least.



Answer :

mhanifa

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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