Difference between revisions of "2007 iTest Problems/Problem 10"
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== Solution == | == Solution == | ||
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+ | Let the youngest grandparent's age be <math>x</math>. The youngest grandparent must be a woman because each grandfather is two years older than his wife. That means the oldest grandparent's age (a grandfather) is <math>x+4</math>, the older grandmother's age is <math>x+2</math>, and the younger grandfather's age is <math>x+2</math>. Because Bertha is younger than Dolores, Bertha is the youngest grandparent of them all. Since the average age of the grandparents is <math>\frac{x + (x+2) + (x+2) + (x+4)}{4} = x+2</math>, the difference between Bertha's age and the mean of the grandparents' ages is <math>\boxed{\textbf{(C) }2}</math> years. | ||
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+ | ==See Also== | ||
+ | {{iTest box|year=2007|num-b=9|num-a=11}} | ||
+ | |||
+ | [[Category:Introductory Algebra Problems]] |
Revision as of 19:48, 17 June 2018
Problem
My grandparents are Arthur, Bertha, Christoph, and Dolores. My oldest grandparent is only years older than my youngest grandparent. Each grandfather is two years older than his wife. If Bertha is younger than Dolores, what is the difference between Bertha’s age and the mean of my grandparents’ ages?
Solution
Let the youngest grandparent's age be . The youngest grandparent must be a woman because each grandfather is two years older than his wife. That means the oldest grandparent's age (a grandfather) is , the older grandmother's age is , and the younger grandfather's age is . Because Bertha is younger than Dolores, Bertha is the youngest grandparent of them all. Since the average age of the grandparents is , the difference between Bertha's age and the mean of the grandparents' ages is years.
See Also
2007 iTest (Problems) | ||
Preceded by: Problem 9 |
Followed by: Problem 11 | |
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