Page 158 - Math Course 2 (Book 2)

Understanding Weighted Averages
Mo. 11

Lesson 3 mixture problem

a problem in which two or more parts are
combined into a whole. These are solved
using weighted averages.
KEY CONCEPTS:

1. Solve mixture problems. Price per
2. Solve uniform motion problems. Units(lb) Unit (lb) Total Price

Dried Fruit 10 $5.50 5.50(10)

Mixed Fruits w $4.75 4.75w
MO. 11 - L3a
Trail Mix 10 + w $4.95 4.95(10 + w)
Solving Mixture Problems

Vocabulary A-Z Let’s Begin

Let us learn some vocabulary

Prices
weighted averages
is the sum of the product of the number of units Examples
(estimate) and the value per unit (weight) divided
by the sum of the number of units (weights).

PETS
Weighted Average Jeri feeds her cat gourmet cat food that costs
$1.75 per pound. She combines it with cheaper
sum of estimate × weight food that costs $0.50 per pound. How many
=
sum of weights pounds of cheaper food should Jeri buy to go
with 5 pounds of gourmet food, if she wants the
Weighted Average average price to be $1.00 per pound?
To demonstrate, let’s make the value of letter tiles in
the popular game Scrabble. Let w = the number of pounds of cheaper cat
food. Make a table.
Value: 10 8 5 4 3 2 1 0
Occurrences: 2 2 1 10 8 7 68 2
Price per
Units(lb) Total Price
To average these values, do a weighted average us- Unit
ing the number of occurrences of each value as the Gourmet cat
weight. To calculate a weighted average. food 5 $1.75 8.75

1. Multiply each value by its weight (Ans: 20, 16, 5, Cheap cat w $0.50 0.5w
40, 24, 14, 68, and 0) food
Mixed cat 5 + w $1.00 1.00(5 + w)
2. Add up the products of value times weight to get food
the total value. (Ans: Sum = 187).
Write and solve an equation using the information
3. Add the weight themselves to get the total weight. in the table.
(Ans: Sum = 100)
Price of price of price of
4. Divide the total value by the total weight gourmet cheaper mixed
(Ans: 187/100 = 1.87 = average value of a cat food plus cat food equals cat food.
scrabble tile ) 8.75 + 0.5w = 1.00(5 + w)

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