Chime Strike Clock
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algebra 2 question...help?
1.The front row of a theater has 25 seats. Each of the other rows has two more seats than the row before it. How many seats are there altogether in the first 20 rows?
2.Kristen is given a test consisting of 15 questions. The first question is worth 5 points, and each question after the first is worth three points more than the question before it.What is the maximum score that kristen can obtain?
3. Every hour a clock chimes as many times as the hour. How many times does it chime from 1 A.M. through midnight, inclusive?
4. A ship's clock strikes every half hour of a 4-hour period. After the first half hour it strikes "one bell," after the second half hour it strikes "two bells," and so on until it strikes "eight bells" at the end of the 4-hour period. How many strikes of the bell occur in one day?
Hi belanova,
For question 1.,
Basically, we are trying to find 25 + (25 + 2) + (25 + 2 + 2) + .... + (25 + 2 + 2 + .... + 2).
We can rearrange the equation a bit to get 25(20) + (2 + 4 + 6 + .... + 38).
(2 + 4 + 6 + .... + 38) = (38 + 2)(38 / 4) = 380
Hence, the total amount of seats is 380 + 25(20) = 380 + 500 = 880 seats.
For question 2.,
Kristen will get the maximum points if he/she gets all the questions correct.
Hence, the maximum number of points is 5 + (5 + 3) + (5 + 3 + 3) + ..... + (5 + 3 + 3 + .... + 3).
We will rearrange the equation as per before to get 5(15) + (3 + 6 + 9 + .... + 42).
(3 + 6 + 9 + .... + 42) = (42 + 3)(42 / 6) = 315
Hence, the maximum amount of points is 315 + 5(15) = 315 + 75 = 390 points.
For question 3.,
What we are trying to find this time round is basically:
1 + 2 + 3 + .... + 11 + 12 + 1 + 2 + .... + 11 + 12
Note that midnight is 12am, and after 11am we have 12pm, not 12 am.
Rearranging the equation above, we have 2(1 + 2 + 3 + .... + 12)
1 + 2 + 3 + .... + 12 = (12 + 1)(12 / 2) = 78
Hence, the amount of chimes is 2(78) = 156 chimes.
For question 4.,
There are 24 hours in one day, and thus 48 half-hours in one day.
The first half hour will have 1 strike, the second half hour will have 2 strikes, the eighth half hour will have 8 strikes. Thus, each half hour will have 1 more strike than the previous one.
What we need to find is : 1 + 2 + 3 + 4 + .... + 46 + 47 + 48.
1 + 2 + 3 + ... + 47 + 48 = (1 + 48)(48 / 2) = 1176 strikes.
Cheers.
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