PROBLEM # 1

How many positive integers less than 100 have a remainder of 3 when dvided by 7?

PROBLEM # 2

Maria has 2 electronic beepers. One of them beeps every 4 seconds, the other beeps every 9 seconds. If they are turned on at the same exact time, how many times during the next hour will both beepers beep together?

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SOLUTIONS TO PROBLEMS ON 7/03/03

PROBLEM # 1

There are 27 students in a Chemistry class and 22 students in physics class. Seven of these students take Physics and Chemistry. What is the ratio of the number of students taking only physics to those taking chemistry?

SOLUTION

Note that 7 students take both subjects. 20 students that take chemistry only and 15 students take physics only. The ratio of those taking physics only to those taking chemistry only is 15/20 or 3:4.

PROBLEM # 2

There are 200 questions on a 3-hour examination. Among these questions are 50 mathematics problems. It is suggested that twice as much time be allowed for each mathematics problem as for each of the other questions. How many minutes should be spent on the mathematics problems?

SOLUTION

Let x be the number of minutes allowed for each of the questions other than the mathematics problems. Then 2x = number of minutes allowed for each mathematics problem. 50 (2x) or 100x = number of minutes allowed for all mathematics problems. 150 x = number of minutes allowed for all other questions.
100x + 150x = total time = 3 hours = 180 minutes
100x + 150 x = 180
250x = 180
x = 180/250
100x = (180/250)100 = 72 minutes

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