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Monday, June 7, 2010

Today's Teaser..............

The local historical society has leased a castle to use it as a museum. The original lease was 99 years. I asked the curator how much time was left on the lease. His answer was as follows: two-thirds of the time past is equal to four- fifths of the time to come. How much time was left on the lease?

4 comments:

Jim (Jimbo) (Jing) said...

Answer; 45 years!

Jim (Jimbo) (Jing) said...

Let X equal the number of years remaining on the lease.

Since there are originally 99 years, then the "time past" is equal to 99 - X.

From the puzzle then, we have:
(2/3) * (99 - X) = (4/5) * X

Distribute the 2/3 over the 99-X:

66 - (2/3)*X = (4/5)*X

Put all the X's on one side:

66 = (2/3 + 4/5)*X

multiply everything by 15 to get rid of the fractions:

990 = (10 + 12)*X

Reduce:

990 = 22*X

Divide both sides by 22:

X = 45.

Therefore, there are 45 years left on the lease, which is now 54 years old.


(To check: 4/5 of 45 is 4*9=36. And 2/3 of 54 is 2*18=36)

Leesh said...

I kwew that....tee hee hee

debadee said...

algebra not my forte, now give me music, word games, and others and I will kick butt!!! LOL