SOLUTION: GEORGE WASHINGTON WAS BORN ON 2/22/1732. HE DIED IN 1799 AT THE AGE OF 67. THE MONTH ON WHICH HE DIED AND THE DAY OF THE MONTH ON WHICH HE DIED ARE CONSECUTIVE EVEN INTEGERS WHOSE

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: GEORGE WASHINGTON WAS BORN ON 2/22/1732. HE DIED IN 1799 AT THE AGE OF 67. THE MONTH ON WHICH HE DIED AND THE DAY OF THE MONTH ON WHICH HE DIED ARE CONSECUTIVE EVEN INTEGERS WHOSE      Log On


   

Question 133454: GEORGE WASHINGTON WAS BORN ON 2/22/1732. HE DIED IN 1799 AT THE AGE OF 67. THE MONTH ON WHICH HE DIED AND THE DAY OF THE MONTH ON WHICH HE DIED ARE CONSECUTIVE EVEN INTEGERS WHOSE PRODUCT IS 168. GIVE THE MONTH/DAY/YEAR WHICH WASHINGTON DIED.
Answer by solver91311(24713) About Me  (Show Source):
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First thing: Please don't write your questions using all caps. It is rude, annoying, and the electronic communications equivalent of shouting.

If n is one even integer, then the next consecutive even integer must be n + 2. The product of n and n + 2 is n%28n%2B2%29=n%5E2%2B2n and we are given that this is equal to 168, so:

n%5E2%2B2n=168

n%5E2%2B2n-168=0

Factor:
14+%2A+-12+=+-168 and 14-12=2, so:

%28n%2B14%29%28n-12%29=0 and n = -14 or n = 12. -14 doesn't make much sense when we are looking for the number of a month. We must have introduced an extraneous root by squaring the variable when we set up the problem. So exclude that value. The remaining value, 12, is then the even integer that corresponds to the month and then next consecutive even integer is 14. Therefore, George Washington died on December 14, 1799.

Check:
12 is an even integer and 14 is the next consecutive even integer and finally, 12 * 14 = 168.