Rational Expressions Test (Study Guide #2)

1. Rational Expressions Test (Study Guide #2) Name_________________1 Simplify 3) 1) 2) 4) 5) 6) 8) 9) 7) Solve: 10) 12) 11) 14) 15) Working together, Anne and Nichole can wallpaper an apartment in 12 hours. It would take Nichole 30 hours to do the job by herself. How long would it take Anne to do the job alone? 17) 16) 18) Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute. It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed? 19) Trader Joe’s has 200 lbs. of mixed nuts that is 10% peanuts. They want to create a trail mix that is 25% peanuts. How many pounds of peanuts must they add to the original mixed nuts? 20)

2. Rational Expressions Test (Study Guide #2) Name_________________1 Simplify 3) 2) 1) 4) 5) 6) 8) 9) 7) Solve: 10) 12) 11) 14) 15) 13) Working together, Anne and Nichole can wallpaper an apartment in 12 hours. It would take Nichole 30 hours to do the job by herself. How long would it take Anne to do the job alone? 17) 16) 18) Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute. It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed? 19) Trader Joe’s has 200 lbs. of mixed nuts that is 10% peanuts. They want to create a trail mix that is 25% peanuts. How many pounds of peanuts must they add to the original mixed nuts? 20)

3. Simplify #1 Factor Cancel Common Factors! Factor

4. Simplify #2 Factor Factor Cancel Common Factors!

5. Multiply #3 Factor Cancel Common Factors!

6. Multiply #4 Cancel Common Factors!

7. Divide = Multiply by the reciprocal of the divisor #5 Cancel Common Factors!

8. Add #6 C.L.T. Cancel Common Factors!

9. Subtract #7 Find a common denominator

10. Add #8 C.L.T. Find a common denominator

11. Subtract #9 Remember to distribute the negative when subtracting! Find a common denominator

12. Solve #10

13. #11 Solve

14. #12 Solve

15. Solve #13 Move terms with common denominator to one side of the equation This problem could have also been solved by multiplying both sides of the original equation by the common denominator of 2x and (x – 2)

16. #14 Solve

17. #15 Solve

18. Solve #16

19. #17 Working together, Anne and Nichole can wallpaper an apartment in 12 hours. It would take Nichole 30 hours to do the job by herself. How long would it take Anne to do the job alone? x = hours it takes for Anne to do the job alone.

20. It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed? #18 x = speed of Jones car x - 15 135 Smith x 180 Jones

21. It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed? #18 x = speed of Jones car

22. Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute. #1

23. Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute. #19 Multiply both sides by 35x

24. #20 Trader Joe’s has 200 lbs. of mixed nuts that is 10% peanuts. They want to create a trail mix that is 25% peanuts. How many pounds of peanuts must they add to the original mixed nuts? “stuff” x = lbs. of peanuts to be added. “stuff” Total Mix Peanuts “have” Original “want” New