Thread: calender

The parliament of the land of Achronia consists of two houses. The parliament was elected in 1995 for a period of fours years beginning pn Monday, January 1st, 1996, when the two houses had their first sessions. According to the rules, the meetings of the first house must occur every ten days for the duration of the term, and the meetings of the second house must occur every twelve days. For example, the second meetings of the first and the second houses were held on the 11th and 13th of January respectitively. A new law can be passed only when both houses meet on a Monday. How many opportunities will the parliament members have to pass new laws during this four year term?

This is easy but i am in Yr 8 so explain the answer clearly to me thx!!!

Hello, claudeluvstwilight!

The parliament of the land of Achronia consists of two houses. The parliament was elected
in 1995 for a period of fours years beginning on Monday, January 1st, 1996, when the two
houses had their first sessions. According to the rules, the meetings of the first house must
occur every ten days for the duration of the term, and the meetings of the second house
must occur every twelve days. For example, the second meetings of the first and the second
houses were held on the 11th and 13th of January respectively.

A new law can be passed only when both houses meet on a Monday.
How many opportunities will the parliament members have to pass new laws
during this four-year term?

The first house meets every 10 days, the second house every 12 days.
They meet simultaneously every 60 days,
. . where 60 is the Least Common Multiple (LCM) of 10 and 12.

They meet together on a Monday every 420 days . . . the LCM of 60 and 7.

Hence, the Monday joint meetings occur on: .
. . during the 4-year (1460-day) term.

Therefore, there are four law-making days.

hi sorobon...

i understand how u got to that answer of 4 law making days but how did u know to find the LCM of 60 and 7. where did the 7 come from??

thx, claude

Originally Posted by claudeluvstwilight

hi sorobon...

i understand how u got to that answer of 4 law making days but how did u know to find the LCM of 60 and 7. where did the 7 come from??

thx, claude

Monday occurs every 7 days. 60 days is the day at which the two house meet at the same time. Hence, you are to find the lowest common multiple at which it will be a Monday (occuring every 7 days) and when they both meet (occuring every 60 days) which is 420 days (so every 420 days, it will be a Monday, and both house will meet).