word problem

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Psychguy98

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On the first week of the year 2000, the twelfth week of the year, and every eleventh week thereafter, John washed his car. On the first week of the year 2000, the tenth week, and every ninth week thereafter, John went camping. How many weeks in 2000 did John both wash his car and go camping?


Do i first have to multiple two things and then divide?
 
Psychguy98 said:
On the first week of the year 2000, the twelfth week of the year, and every eleventh week thereafter, John washed his car. On the first week of the year 2000, the tenth week, and every ninth week thereafter, John went camping. How many weeks in 2000 did John both wash his car and go camping?


Do i first have to multiple two things and then divide? <<< What does that mean?
Click to expand...
 
Hello, Psychguy98!

The problem is rather silly . . . The answer is even sillier.

On the first week of the year 2000, the twelfth week of the year, and every eleventh week thereafter, John washed his car.
On the first week of the year 2000, the tenth week, and every ninth week thereafter, John went camping.
How many weeks in 2000 did John both wash his car and go camping?
Click to expand...

The LCD of 11 and 9 is: .\(\displaystyle 11\cdot9 \,=\,99\)

In the first week of 2000, John washed his car and went camping.
Every ninety-nine weeks thereafter, he does both activities.
99 weeks? . . . That's almost two years!

He did both activities only ONCE during 2000.
. . (The next time is early December 2001.)

 
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