1. Resource –Glencoe Algebra 1
Equation Part 5
Resource –Glencoe Algebra 1

2. Section 2.9
Weighted Average M of a set of data is the sum of the product of the numbers of units and the value per unit divided by the sum of the numbers of units.
Mixture problems- are problems in which two or more parts are combined into a whole.

3. Real –World Example 1 Mixture Problem
Retail- A tea company sells blended tea for $ 25 per pound. To make blackberry tea, dried blackberries that cost per pound are blended with black tea that cost $35 per pound. How many pounds of black tea should be added to 5 pounds of dried blackberries to make blackberry tea?

4. Mixture Problem- Tea Dried Blackberries 5 10.50 10.50(5) Black Tea w
Number of Units (b)
Price per unit ($)
Total Price
Dried Blackberries 5
10.50
10.50(5)
Black Tea w 35
35w
Blackberry Tea
5+w 25
25(5+w)

5. Example 1 10.50(5) +35w=25(5+w) 52.5 +35w=125 +25w

6. Example 2 Percent Mixture Problem
Fruit Punch- Mrs. Matthews has 16 cups of punch that is 3% pineapple juice. She also has a punch that is 33% pineapple juice. How many cups of the 33% punch will she need to add to the 3% punch to obtain a punch that is 20% pineapple juice?

7. Real –World Example 2 Amount of Punch (cups) Amount of Pineapple Juice16
0.03(16)
33% Punch X
0.33X
20% Punch
16+X
0.2(16+X)

8. EXAMPLE 2 CONTINUE 0.03(16) +0.33X= 0.20(16+X) 0.48 +0.33X=3.2 +0.20X
X=20.9

9. UNIFORM MOTION PROBLEM
UNFORM IN MOTION PROBLEM – ARE PROBLEMS IN WHICH AN OBJECT MOVES AT A CERTAIN SPEED OR RATE. THE FORMULA D=RT IS USED TO SOLVE THESE PROBLEMS. IN THE FORMULA, D= REPRESENTS DISTANCE, R=REPRESENT RATE AND T REPRESENT TIME.

10. Real World Example 3 Problem (Round Trip)
INLINE SKATING – It took Travis and Tony 40 minutes to skate 5 miles. The return trip took them 30 minutes. What was their average speed for the trip?
Hint 30/ minutes equal a half of hour or
40/ minutes equal 0.667hours

11. Speed of One Vehicle
Rate
Time
Distance
Going r
0.667 5
Return
0.5

12. Continue … R*T=D or R=D/T r*0.667=5 r=5/0.667 r=7.5 miles
R=8.6

13. Real World Example 4
Freight Trains- Two trains are 550 miles apart heading toward each other on parallel tracks. Train A is traveling east at 35 miles per hour, while Train B travels west at 45 miles per hour. When will the trains pass each other.

14. Continue … R T D
Train A 35 t
35t
Train B 45
45t

15. Speeds of Two Vehicles continue…
35t + 45t= 550
80t =550
t= hours

16. Problem 5 Opposite Direction
Jane and Peter leave their home travelling in opposite directions on a straight road. Peter drives 15 mi/h faster than Jane. After 3 hours, they are 225 miles apart. Find Peter’s rate and Jane’s rate.

17. Problem 5 continue Person Rate Time Distance Jane r 3 3r Peter r+5

18. Problem 5 continue… 3r+3(r+15)=225 3r +3r +45=225 6r+45=225 6r=180

19. Consecutive Integers
The sum of three consecutive integers is 147. Find the integers.
Let n =the first integer
Then n+1 the second integer
And n+2 =third integer
n+ n+1+n+2 =147
3n +3 =147
3n=144
N=48

20. Geometry
The length of a rectangle is 6 in more than its width. The perimeter of the rectangle is 24 in. What is the length of the rectangle?
W=width
W+6 =length
P=2l +2w