Weighted Averages

Algebra Chapter 3 section 9

Mixture Problems

Yummy Cookie Company sells chocolate chip cookies for $6.95 per pound and white chocolate cookies for $5.95 per pound. How many pounds of chocolate chip cookies should be mixed with 4 pounds of white chocolate cookies to obtain a mixture that sells for $6.75 per pound.

Fill in chart

c

# of pounds

Price per pound

Total price

Chocolate chip

White Chocolate

Mixture

$6.95 $6.95c

$5.95 $5.95(4)

$6.75 $6.75(c+4)

4

c+4

Set up your equation• Use the last column to create an

algebraic equation:

6.95c + 5.95(4) = 6.75(c + 4)

Now use your expert skills to solve for the variable … what do you get for w?

c = 16, so 16 pounds of chocolate chip cookies need to be mixed with 4 pounds of white chocolate cookies

6.95c + 23.80 = 6.75c + 27

Try another one …

Example #2:

The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound and walnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15 pounds of pecans to make a mixture that sells for $1.75 per pound?

Fill in chart

Walnuts

Pecans

Mixture

# of pound

s

Price per

pound

Total Price

$1.95

$1.55

$1.75

w

15

w+15

1.55(15)

1.95w

1.75(w+15)

Set up your equation• Use the last column to create an

algebraic equation:

15(1.55) + 1.95w = 1.75(w + 15)Again … use your expert skills to solve for the variable … what do you get for w?

w = 15, so 15 pounds of walnuts need to be mixed with 15 pounds of pecans to make the $1.75 per pound mixture

23.25 + 1.95w = 1.75w + 26.25

Mixtures with percentsHow many quarts of pure orange juice should Mike add to a 10% orange drink to create 6 quarts of a 40% orange juice mixture? Let p represent the number of quarts of pure orange juice he should add to the orange drink.

Fill me in …

Orange juice

Orange drink

Orange mixture

Quarts Amt of juice% of

solution

100% = 1

10%=0.1

40%=0.4

p

6 - p

1p

0.1(6 – p)

0.4(6)6

Set up your equation• Use the last column to create an

algebraic equation:

1p + 0.1(6 – p) = 0.4(6)Again … use your skills to solve for p …1p + 0.6 – 0.1p = 2.4

0.9p = 1.8 p = 2 qts

So, 2 quarts of pure oj added to 4 qts of 10% oj will result in 6 qts of 40% oj

Rate Problems (d = rt)

• At 7:00 am, two groups of hikers begin 21 miles apart and head toward each other. The first group, hiking at an average rate of 1.5 miles per hour, carries tents, sleeping bags and cooking equipment. The second group, hiking at an average rate of 2 miles per hour, carries food and water. Let t represent the hiking time.

Create and fill in chart

r t d = rt

First group of hikers

Second group of hikers

1.5

2

t

t

1.5 t

2 t

21 miles

Set up your equation

Use the last column to create an algebraic equation:

1.5 t + 2 t = 21Solve for t 3.5 t = 21 (divide both sides by 3.5)

t = 6 what does that mean?

The time it took for the two groups to meet took 6 hours.

? How far did the first group of hikers hike …?

Rate Problems (d = rt)

• Two city buses leave their station at the same time, one heading east and one heading west. The eastbound bus travels at 35 miles per hour, and the westbound bus travels at 45 miles per hour. In how many hours will they be 120 miles apart?

Create and fill in chart

Eastbound Bus

r t d = rt

Westbound Bus

35

45

t

t

35 t

45 t

120 miles

Set up your equation

Use the last column to create an algebraic equation:

35 t + 45 t = 120Solve for t 80 t = 120 (divide both sides by 80)

t = 1.5 what does that mean?

The time it took for the two buses to be 120 miles apart took 1.5 hours.

? How far did the Eastbound bus travel …?

Espresso or Cappuccino?Suppose the Central Perk coffee Shop sells a cup of espresso for $2.00 and a cup of cappuccino for $2.50. On Friday Rachel sold 30 more cups of cappuccino than espresso , and she sold $178.50 worth of espresso and cappuccino. How many cups of each were sold?

Fill me in …