After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets?

Question

Accepted Answer

Let the total number of sweets be (25x + 8).

Then, (25x + 8) - 22 is divisible by 28

⟺ (25x - 14) is divisible by 28 ⟺ 28x - (3x + 14) is divisible by 28

⟺ (3x + 14) is divisible by 28 ⟺ x = 14.

After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets?

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