Grades 5-6 Video Solutions 2015-Level 5&6 Video Solutions 2015 problem14

Level 5&6 Video Solutions 2015 problem14

Video Transcription

Question number 14. Lucy and her mother were both born in February. On March 19, 2015, Lucy adds the year of her birth, the year of her mother's birth, her age, and her mother's age. What result does she get?  We're talking about dates here, so let's draw a timeline representing Lucy's birth date and the current year on opposite ends.  So let's have here Lucy's birth, the beginning of this timeline, so that would be February of some year, we don't know exactly what year.  Let's have here then a landmark year, and the end would be today.  And by today I mean the date of the contest, so March 19, 2015, and here this landmark is going to be Lucy's current birth date, and that is in February of 2015.  So Lucy is adding the year of her birth, so that is an unknown, together with her age, and her age we can mark here on this timeline.  That is exactly the distance separating her birth with her most recent birth date, so that is Lucy's age, which we also don't know, but together that sum, the year of your birth together with your current age, on a day past your most recent birth date, well that is the number that we call 2015.  We're talking about this particular problem, and that should make sense. Subtract from the current year your age, and that should give you the year of your birth, and the calculation would be the same for Lucy as for her mother.  Either addition of the year in which they were born to their current age would result in 2015, so to solve the problem we have to double that, and let's write this down.  We have Lucy's age plus her year of birth, and that is equal to 2015, and then same thing for her mother.  Lucy's mother's age plus her year of birth, that is also by the same calculation, 2015. Doubling 2015 gives us answer C, 4030.

Video Summary

The problem involves calculating Lucy and her mother's combined birth years and ages as of March 19, 2015. Lucy was born in February of an unknown year, and on March 19, 2015, her age plus her birth year equals 2015. Similarly, her mother's age plus birth year also equals 2015. The key is that both combinations yield 2015, so their combined sum (adding both their ages and birth years) is doubled: 2015 + 2015 = 4030. Therefore, the result Lucy obtains is 4030.