Emily wants to become a professional chef, but the cooking school she wants to apply to only accepts applicants over 17. Here's what you know about Emily's siblings' ages: 1) Emily's brother Patrick's age is two times that of Emily, and; 2) Emily's sister Nicole's age is one-half of that of Patrick. Nicole turned 17 this year. Using this information, can Emily apply to the cooking school this year?
Think about the age chain: Nicole → Patrick → Emily. If Nicole is 17, what can you say about Patrick's age, and then about Emily's age?
No, she cannot. If Nicole is 17, and her age is one-half of that of Patrick, then Patrick must be two times Nicole's age. Therefore, Patrick is 34. If Patrick is 34, and his age is two times that of Emily, then Emily must be one-half of Patrick's age. Therefore, Emily is 17. Emily and Nicole are of the same age because they are twins. However, the cooking school only accepts applicants "over 17", not "17 and over". Therefore, Emily cannot apply to the cooking school this year.
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