Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Prove it North Macedonia

One student was multiplying two numbers. During the multiplication he switched the last digit of the first number, which was $4$ , with $1$ . So he obtained $525$ as a result instead of $600$ . Which numbers did the student multiply?

Solution

From the condition in the problem we get that when the first number is reduced by $4-1=3$ , then their product is reduced by $600-525=75$ . So the second number is $75 \div 3 = 25$ . The first number is $600 \div 25 = 24$ . The numbers are $24$ and $25$ .

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