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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?

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?

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?

4. Find the roots.

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

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Mixture Problems

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? Component #1 Component #2 Mixture + = A=amountP=percent.925x.925x.90y.90y Sterling Silver Silver Alloy

Component #1 Component #2 Mixture + = A=amountP=percent.925x.925x.90y.90y x + y = x +.90y = 455 Sterling Silver Silver Alloy

x + y = x +.90y = 455 – 900x – 900y = – x + 900y = x = 5000 x = 200grams

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

x + y = 35.04x +.11y = % 11% 7% mix + = A=amountP=percent.04x.04x.11y.11y

x + y = 35.04x +.11y = 2.45 –4x – 4y = –140 4x + 11y = y = 105 y = 15gallons x + 15 = 35 x = 20 gallons

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=amountP=percent x 0 0.1y 0.1y 10% mix + = 50% solution Water (0%)

40 + x = y = 0.1y 10% mix + = A=amountP=percent x 0 0.1y 0.1y 50% solution original

20 = 0.1y 40 + x = y 40 + x = = y 10 x = 160mL

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%? 3% 10% 8% Mix + = A=amountP=percent.03x.03x y.08y

x + 60 = y.03x + 6 =.08y 3% 10% 8% + = A=amountP=percent.03x.03x y.08y

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

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.

x + y = 8.5x + y = % 100% 80% mix + = A=amountP=percent.5x.5x 1y y

x + y = 8.5x + y = 6.4 –10x – 10y = –80 5x + 10y = x = –16 x = 3.2 Yes, you have 4 buckets and only need 3.2