1. Find the quotient of 10 and 2 added to the product of 20 and 2.
2. The formula N=0.07x + 4.1 models the number of women, N, in millions, enrolled in U.S. colleges x years after 1984. How many years after 1984 is the projected enrollment for women expected to reach 6.2 million? In which year is this expected?
3.The optimum heart rate that a person should achieve during exercise for the exercise to be most beneficial is modeled by r =0.6(220-a), where a represents a person's age and r represents that person's optimum heart rate, in beats per minute. If the optimum heart rate is 120 beats per minute, how old is that person?
5. The length of a rectangular parking lot is 10 yards less than twice its width. If the perimeter of the lot is 400 yards, what are its dimensions?
6. To pass a course, you must have a final average of at least 60%. If a student scores 42 and 74 on the first two tests, what must be earned on the third test to pass the course?
7. A rectangular field is three times as long as it is wide. If the perimeter of the field is 400 yards, what are the field's dimensions?
1. Quotient of 10 and 2 = 10/2 = 5
Product of 20 and 2 = 20 x 2 = 40
Quotient of 10 and 2 added to the product of 20 and 2= 40+5=45
2. N=0.07x + 4.1 (N in millions)
N = 6.2
x = (6.2-4.1)/0.07 = 30
Hence, 30 years after 1984 the projected enrollment for women is expected to reach 6.2 million. In the year 2014, (1984+30), this is expected.
3. r =0.6(220-a), where a represents a person's age and r represents that person's optimum heart rate (in beats per minute).
r = 120
Therefore, 120 = 0.6(220-a)
Or, 220-a= 120/0.6 = ...
This solution is comprised of detailed step-by-step calculations and explanation of the given problems and provides students with a clear perspective of the underlying concepts.