Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem9

Video Transcription

Question number nine. It is now the year 2010. During yesterday's math class, the teacher said it was his birthday, and that the product of his age and his father's age is 2010. In what year was the teacher born?  So we know that the product of two ages is exactly 2010. And to recover those numbers, we need to factor 2010. It's always a good idea to be able to factor the contest year number.  And so 2010 factors into, for example, 10 times 201, then 10 factors into 2 and a 5, and 201 into 3 and 67. And this is the prime factorization of 2010.  So we have here 67 is prime, and so that has to be an age. And it must, in fact, be the father's age.  Now, we need two factors, so we multiply here the remaining numbers, and what we have is 2 times 5 times 3 is 30 times 67, where 30 is the son's age or the teacher's.  Age in 2010. So he was born 30 years in the past, so in 2010 minus 30, that gives us the year 1980.  And the answer, therefore, is C. Being 30 years old currently in 2010, the teacher was born in 1980.

Video Summary

The math teacher mentioned that the product of his age in 2010 and his father's age equaled 2010. By factoring 2010 into its prime components (2, 3, 5, and 67), we find ages: 67 (father's age) and 30 (teacher's age). Calculations show the teacher's age is 30, making his birth year 1980 (2010 - 30). Therefore, the teacher was born in 1980.