Section 4.7

What we are Learning:To solve mixture problems

To solve problems involving uniform motion

Weighted Average:

• Find the sum of each weighted area and multiply the sum by the weight of that area. Continue the process till all weights are accounted for. Divide the total by the sum of all the weights.

ScorePerfect of Total

section)for that entries all of m weight(su section)for that entries all of weight(sum

Example:

• Amy’s Algebra I final grade is based on: homework 20%, Quizzes 30%, Chapter Tests 40%, and Final 10%. What will her final grade be based upon this report card?

Area: Weight: Scores: Total Available Points

Homework 20% 100%, 80%, 50%, 100%, 70%, 50%

60

Quizzes 30% 75%, 100%, 40% 60

Chapter Tests 40% 71%, 86% 70

Final 10% 82% 100

Solution:

%55.71290

207502900

820 6280 6450 72002900

10(82) 40(157) 30(215) 20(360)290

)82(10)8671(40)4010075(30)50701005080100(20

Mixture Problem:

• Use weighted averages• The weight is usually:– Price– Percentage of something

Example:

• I am in need of caffeine and I have a coffee drink mix that contains 10% caffeine. I want a drink that contains 30% caffeine in 24oz. How much mix should I use if I also have some pure caffeine drops?

Let p = pure caffeine drops to be added

Ounces Amount of drops

10% caffeine mix 24 - p 0.10(24 – p)

Pure caffeine p 1.00p

30% caffeine 24 .30(24)

Solution:0.10(24 – p) + 1.00p = .30(24)2.4 - .1p + 1.00p = 7.22.4 + .9p = 7.22.4 – 2.4 + .9p = 7.2 – 2.4.9p = 4.8.9p/.9 = 4.8/.9p = 5.33 ounces of caffeine drops

24 – 5.33 = coffee mix needed• I need 8.67 ounces of Coffee mix

Uniform Motion:

• An object that moves at a constant speed or rate

• Also called Rate Problems• d = rt– d: distance– r: rate of speed– t: time

Example:

• Max flew to visit his grandparents over spring break. The distance is 800 miles one way. On the way to his grandparents the plane was able to maintain a speed of 600mph. On the way home the plane hit a head wind and was only able to maintain a speed of 530mph. What is the total time that Max spent flying?

• Round answer to the nearest hundredth

Solution:

• d = rt800 = 600t800/600 = 600t/6001.33 = t

• d = rt800 = 530t800/530 = 530t/5301.51 = t

Time spent flying = 1.33 + 1.51 = 2.84 hours

Let’s Work Together:

• Joshua is doing a chemistry experiment that calls for 30% solution of copper sulfate. He has 40mL of 25% solution. How many milliliters of 60% solution should Joshua add to obtain the required 30% solution?

Amount of Solution (mL)

Amount of Copper Sulfate

25% solution 40

60% solution x

30% solution

Let’s Work Together:

• A bus leaves Twin Falls headed for Boise. It travels the 128 miles in 2.5 hours. A second bus leaves Ontario, Or and travels the 56 miles to Boise in 87 minutes. Which bus was driving faster?

Homework:

• Page 237– 9 to 15 odd