Rate HW Answers

1. Rate HW Answers

2. 1. 2. 3. 4. 5. 6. 7. 8.

3. 9. 10. 11. 12. 13. 14. 15. 16.

4. 17. 18.

5. Scoring Your Homework Count how many problems you missed or didn’t do 0-1 missed = 10 2-3 missed = 9 4-5 missed = 8 6-7 missed = 7 8-9 missed = 6 • 10-11 missed = 5 • 12-13 missed = 4 • 14-15 missed = 3 • 16-17 missed = 2 • 18-19 missed = 1 • 20-21 missed = 0

6. Daily Check • No talking to other groups • Make sure all answers match • Only one is graded

7. 1. Karen has her own business making cloth “ouch-pouches”, little first aid kits with snaps. She assembles them and puts them in a box. It takes Karen 3 hours to put snaps on all the pouches in a box, while her sister Kathy takes 5 hours. How long would it take both of them together to put snaps on one box?

8. 2. Thelma and Louise are driving on a 810 mile trip. Thelma drives for the first 3 hours at an average rate of 60 mi/hr. If Louise takes over for the rest of the trip which takes a total of 12 hours to complete, what is the average rate at which Louise drives?

9. 3. Three identical strips of lawn at Balboa Park need to be mowed. Mo can do the strips in 2 hours using a riding lawn mower. Curly takes 3 hours using a regular walking mower. If they work together, how long will it take for both of them to finish all three strips?

10. 4. Find the roots.

11. 5.Which is one of the solutions to the equation? a. one b. two c. three d. none

12. Turn your hw in!

13. Mixture Problems

14. Ex #1: Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy? A=amount P=percent x .925 .925x Component #1 Sterling Silver + y .90 .90y Component #2 Silver Alloy = 500 .91 455 Mixture

15. A=amount P=percent x .925 .925x Component #1 Sterling Silver + y .90 .90y Component #2 Silver Alloy = 500 .91 455 Mixture x + y = 500 .925x + .90y = 455

16. .925x + .90y = 455 1000 x + y = 500 -900 925x + 900y = 455000 – 900x – 900y = –450000 25x = 5000 x = 200 grams

17. Ex #2: How many gallons each of a 4% and 11% salt solution should be mixed to obtain 35 gallons of a 7% solution? A=amount P=percent Component 1: x .04 .04x 4% + Component 2: y .11 .11y 11% = 35 .07 2.45 7% mix

18. A=amount P=percent x .04 .04x 4% + y .11 .11y 11% = 35 .07 2.45 7% mix x + y = 35 .04x + .11y = 2.45

19. .04x + .11y = 2.45 100 x + y = 35 -4 4x + 11y = 245 –4x – 4y = –140 7y = 105 y = 15 gallons x + 15 = 35 x = 20 gallons

20. Ex #3: A chemist has 40 mL of a solution that is 50% acid. How much water should be added to the original solution to make a solution that is 10% acid? A=amount P=percent 40 0.5 20 50% solution + x 0 0 Water (0%) = y 0.1 0.1y 10% mix

21. A=amount P=percent 40 0.50 20 50% solution + x 0 0 original = y 0.1 0.1y 10% mix 40 + x = y 20 + 0 = 0.1y

22. 40 + x = y 20 = 0.1y 10 200 = y 40 + x = 200 x = 160 mL

23. Ex #4: How many gallons of a 3% acid solution must be mixed with 60 gallons of 10% acid solution to obtain an acid solution that is 8%? A=amount P=percent x .03 .03x 3% + 60 .10 6 10% = y .08 .08y 8% Mix

24. A=amount P=percent x .03 .03x 3% + 60 .10 6 10% = y .08 .08y 8% x + 60 = y .03x + 6 = .08y

25. x + 60 = y .03x + 6 = .08y 100 3x + 600 = 8y 3x + 600 = 8(x + 60) 3x + 600 = 8x + 480 600 = 5x + 480 120 = 5x 24 = x

26. Ex #5: You are creating a potting mix for your window boxes that is 20% peat moss and 80% potting soil. You add 100% potting soil to your mix that is currently 50% peat moss and 50% potting soil. You have 4 buckets of the mix that is half and half. Do you have enough of the half and half mix to make 8 buckets of the mix that is 20% peat moss and 80% potting soil. Explain your answer.

27. A=amount P=percent x .5 .5x 50% + y 1 y 100% = 0.80 8 6.4 80% mix x + y = 8 .5x + y = 6.4

28. .5x + y = 6.4 10 x + y = 8 -10 5x + 10y = 64 –10x – 10y = –80 -5x = –16 x = 3.2 Yes, you have 4 buckets and only need 3.2