The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven piano sonata will be played followed by a Beethoven symphony followed by a Beethoven piano concerto. For how many years could this policy be continued before exactly the same program would have to be repeated? (Assume there are 365 days in a year. Round your answer up to the nearest whole number.)

Question

Mathematics

Yair Bruce

19 February, 07:44

The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven piano sonata will be played followed by a Beethoven symphony followed by a Beethoven piano concerto. For how many years could this policy be continued before exactly the same program would have to be repeated? (Assume there are 365 days in a year. Round your answer up to the nearest whole number.)

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Answers (1)

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Briggs · Answer 1

3 years, 11 months and 10 days

Step-by-step explanation:

Beethoven wrote

32 piano sonatas

9 symphonies

5 piano concertos

By the fundamental principle of counting there are

32 times 9 times 5 ways of combining these pieces in the required order.

32 times 9 times 5 = 1,440

As there are 365 days in a year, the policy decided by the manager could be continued during

1,440/365 = 3.9452 years.

But 3.9452 years = 3 years + 0.9452 years.

As 1 year equals 12 months

0.9452 years = 11.3424 months

11.3424 months = 11 months+0.3424 months

As 1 month = 30 days

0.3424 months = 10.27 days = 10 days rounded to the nearest integer

So, the manager could continue this policy for

3 years, 11 months and 10 days without repeating the program.