Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

Mary's daughter gave birth to a baby girl today. In 2 years time, the product of the ages of Mary, her daughter, and her granddaughter will be 2024.  Mary's and her daughter's ages are both even numbers. What is Mary's age now? We know that the granddaughter will be 2 years old in 2 years time.  Let's let Mary's age be 2M and her daughter's age be 2D. Then we know that the product of the ages will be 2 times 2D times 2M.  We compare this with a prime factorization of 24 which we know is 2 times 2 times 11 times 2 times 23.  Therefore Mary will be 46 in 2 years time and her current age is 44 and our answer is B.

Video Summary

The problem involves determining Mary's current age given a future scenario. Mary's daughter has just given birth to a granddaughter. In two years, their ages' product will be 2024, and the granddaughter will be 2. Let's express Mary's age as 2M and her daughter's age as 2D. In two years, the product of their ages (all even numbers) will be expressed as 2 * 2D * 2M = 2024. Prime factorization of 2024 is 2 * 2 * 11 * 2 * 23, aligning with their age product. Thus, Mary will be 46 in two years, and currently, she is 44.

Keywords

Mary's age

age problem

prime factorization

future scenario

age calculation