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If 6a = 7b = 42c, which of the following statements can be correct?a + b = c1a + 1b = 1c a × b = ca = bc

Question

If 6a = 7b = 42c, which of the following statements can be correct?a + b = c1a + 1b = 1c a × b = ca = bc

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Solution

The given equation is 6a = 7b = 42c.

Let's break it down:

  1. If 6a = 42c, then a = 7c.
  2. If 7b = 42c, then b = 6c.

Now, let's check each statement:

  1. a + b = c: Substituting a and b from above, we get 7c + 6c = c, which simplifies to 13c = c. This is not possible unless c = 0, but if c = 0, then a and b would also have to be 0, which contradicts the original equation. So, this statement is incorrect.

  2. 1a + 1b = 1c: This is the same as the first statement, so it is also incorrect.

  3. a × b = c: Substituting a and b from above, we get (7c) × (6c) = c, which simplifies to 42c^2 = c. This is not possible unless c = 0 or c = 1/42. If c = 0, then a and b would also have to be 0, which contradicts the original equation. If c = 1/42, then a = 7/42 and b = 6/42, which would make the original equation true. So, this statement can be correct.

  4. a = bc: Substituting a and b from above, we get 7c = (6c) × c, which simplifies to 7c = 6c^2. This is not possible unless c = 0 or c = 7/6. If c = 0, then a and b would also have to be 0, which contradicts the original equation. If c = 7/6, then a = 7 and b = 7, which would make the original equation false. So, this statement is incorrect.

Therefore, the only statement that can be correct is a × b = c.

This problem has been solved

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