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# Basic algebra questions in Math 209, week 3

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Please see attached file for full problem descriptions.

1. Reduce each expression to lowest term.

Perform the indicated operation.

2. Henry sold 120 mags subscription in x + 2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?

Find the LCD for the given rational expressions and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

3. Perform the indicated operation. Reduce each answer to lowest terms.

4. Simplify. Reduce to lowest terms.

5. Factor

6. 36z^4 + 12^3 - 8z^2

7. -7w + 7z + zy - yw

8. 18u^4x^5y^5 and 24x^3y^7

9. A well known university, ¼ if the undergraduate students commute, and 1/3 of the graduate students commute. 1/10 of the undergraduate students drive more than 40 miles daily, and 1/6 of the graduate students drive more than 40 miles daily. If there are 2x as many undergraduate students as there are graduate students, what fraction of the commuters drive more than 40 miles daily?

Solve the equation:

10.

11.

12. among coffee drinkers, 36 said that they preferred their coffee black and the rest did not prefer their coffee black. Find the ratio of those who prefer black coffee to those who prefer nonblack coffee.

13. if four out of five doctors prefer fast food, then at a convention of 445 doctors. How many prefer fast food?

14. the ancient greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of the rectangular painting is 2 feet longer than its width, then for what dimensions would the length and width have the golden ratio?

15. to estimate the size of the bear population on the kweenaw peninsula, conservationist captured, tagged, and release 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist estimate of the size of the bear population?

Solve the equation for y:

16.

17. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than smith and his trip took ½ hour longer than Smith's. How fast was each one traveling?

18. a six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind at the same amount of time as it flies 5 miles against the wind, then what is the wind speed?

19. A water tank has an inlet pipe and a drain pipe. A full tank ca be emptied in 30 mins if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank.

20. Under what situation would one or more solutions of a rational equation be unacceptable? Give example

21 In what sense do exponentials and radicals behave exactly the same way? Give example.