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

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.

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 10.50 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?

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)

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

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?

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

EXAMPLE 2 CONTINUE 0.03(16) +0.33X= 0.20(16+X) 0.48 +0.33X=3.2 +0.20X 0.13 0.13 X=20.9

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.

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 30/60 30 minutes equal a half of hour or 0.5 40/60 40 minutes equal 0.667hours

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

Continue … R*T=D or R=D/T r*0.667=5 r=5/0.667 r=7.5 miles 1.167 1.167 R=8.6

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.

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

Speeds of Two Vehicles continue… 35t + 45t= 550 80t =550 80 80 t= 6.875 hours

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.

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

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

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

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