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 equally distributing. What was the total number of sweets?
(a)328
(b)348
(c)358
(d)Data inadequate
Answer
Answer (as printed): C
Explanation
Let the total number of sweets be $(25x+8)$. Then, $(25x+8)-22$ is divisible by $28 \Leftrightarrow (25x-14)$ is divisible by $28 \Leftrightarrow 28x-(3x+14)$ is divisible by $28 \Leftrightarrow (3x+14)$ is divisible by $28 \Leftrightarrow x=14$. Total number of sweets $=(25 \times 14+8)=358$.
Explanation as extracted from the printed page; notation may be imperfect.