Page 397 - Basic College Mathematics with Early Integers

5.3 PROPORTIONS AND PROBLEM SOLVING
Objective

Solve Problems by Writing
Proportions.
Objective Solving Problems by Writing Proportions
Writing proportions is a powerful tool for solving problems in almost every field,
including business, chemistry, biology, health sciences, and engineering, as well as in
daily life. Given a specified ratio (or rate) of two quantities, a proportion can be
used to determine an unknown quantity.
In this section, we use the same problem-solving steps that we have used earlier
in this text.

PRACTICE 1 Example 1 Determining Distances from a Map
On an architect’s blueprint, On a chamber of commerce map of Abita Springs, 5 miles corresponds to 2 inches.
1 inch corresponds to 4 feet. How many miles correspond to 7 inches?
How long is a wall represented
1
by a 4 -inch line on the Nursery St Dogwood S SuccessSt Carnation St 59
Camelia St
4 Boxwood St PansySt Jasmine St Dahlia St 435 Holly Oak
blueprint? Nursery St AzaleaSt Rose St Violet St Daisy St A51 DavisCemetery R d Long Branch 2 inches 5 miles Cryer Rd Vine St E Dr N
Ahmeek Ln
Vine St
Gurtner Dr Jackie Ln M artinLn Kustenmacher Rd Gordon Ave 36 Abita River North St
Tammany Trace Miller Ln Oak St Burvant St
North St Forest Hill Dr
Kustenmacher Rd Holly St Railroad Ave Hickory St Gum St Main St Pine St Magnolia St Level St Indian Trail Cherry Julia St V & M Rd
Kus t St Kust St Live Oak St Grover St
Cypress St
2nd St Leveson St GroverSt Regina St Lange Rd
Peters S Lawrence Ln
3rd St Bossier Av Eads St Eads S Eads St
Laurel St
Maple St
St Mary St
Andrews St
Kust St
5th St Hutchinson St
6th St
59 St John St Danny Park Dr
6th St
Pearl St Keller St Leveson S 7th St St James St
7th St St Joseph St 8th St 36
Mary S
0 1 mi
8th St
Haynes St
Orme St Abita–Mandeville Hwy Hickory Hwy
St Mary St
9th St Nightwalk 0 1 km
Heintz Gordon Ave St St Ann St 10th St
10th St 10th St 9th St St Charles St
Poitevent Ave
Stire St Keller St Dundee Rd ABITA SPRINGS
11th St
Millar St Leveson St St John St
12th St
Cherokee Dr
Solution:
1. UNDERSTAND. Read and reread the problem. You may want to draw a
diagram.
between 15 and 20 miles
15 miles
20 miles
5 miles 5 miles 5 miles 5 miles =a little over 15 miles
2 inches 2 inches 2 inches 2 inches =7 inches
8 inches
6 inches
7 inches
From the diagram we can see that a reasonable solution should be between 15
and 20 miles.
2. TRANSLATE. We will let n represent our unknown number. Since 5 miles
corresponds to 2 inches as n miles corresponds to 7 inches,we have the proportion
miles : 5 = n ; miles
inches : 2 7 ; inches
3. SOLVE: In earlier sections, we estimated to obtain a reasonable answer.
Notice we did this in Step 1 above.
5 = n Copyright 2012 Pearson Education, Inc.
2 7
Answer
1. 17 ft
374