Page 271 - Basic College Mathematics with Early Integers

248 C HAPTE R 3 I FRACTIONS

Objective Solving Problems Containing Mixed Numbers

Now that we know how to perform operations on mixed numbers, we can solve
real-life problems.

PRACTICE 15 Example 15 Finding Legal Lobster Size
The measurement around the Lobster fishermen must measure the upper
trunk of a tree just below body shells of the lobsters they catch.
shoulder height is called its Lobsters that are too small are thrown back
girth.The largest known into the ocean. Each state has its own size
American beech tree in the standard for lobsters to help control the
United States has a girth of breeding stock. Massachusetts divided its
1 waters into four Lobster Conservation
23 feet. The largest known
4 Management Areas, with a different minimum lobster size permitted in each area.
sugar maple tree in the United 13
5 In the offshore area, the legal lobster size increased from 3 32 inches in 2006 to
States has a girth of 19 feet. 1
12 3 inches in 2008. How much of an increase was this? (Source: Massachusetts
How much larger is the girth of 2
Division of Marine Fisheries)
the largest known American
beech tree than the girth of the Solution:
largest known sugar maple
1. UNDERSTAND. Read and reread the problem carefully. The word “increase”
tree? (Source:American
found in the problem might make you think that we add to solve the problem.
Forests)
But the phrase “how much of an increase” tells us to subtract to find the increase.
2. TRANSLATE.
new old
In words: increase is lobster minus lobster
size size

T T T T T
Girth
1 13
Translate: increase = 3 - 3
2 32
3. SOLVE. Before we solve, let’s estimate by rounding to the nearest wholes.The
1 13
fraction 3 can be rounded up to 4, 3 rounds to 3, and 4 - 3 = 1. The
2 32
1 13
increase is not 1, but will be smaller since we rounded 3 up and rounded 3
2 32
down.
1 16
3 = 3
2 32
13 13
- 3 =- 3
32 32
3

32
4. INTERPRET. Check your work. Our estimate tells us that the exact increase
PRACTICE 16 3 3
of is reasonable. State your conclusion: The increase in lobster size is of
A designer of women’s clothing 32 32
designs a woman’s dress that an inch.
1
requires 3 yards of material. Work Practice 15
7
How many dresses can be
made from a 44-yard bolt of Example 16 Calculating Manufacturing Materials Needed Copyright 2012 Pearson Education, Inc.
material? 3
In a manufacturing process, a metal-cutting machine cuts strips 1 inches long
Answers 5
from a piece of metal stock. How many such strips can be cut from a 48-inch piece
5
15. 3 ft 16. 14 dresses
6 of stock?