Page 398 - Basic College Mathematics with Early Integers

S E C T I O N 5.3 I PROPORTIONS AND PROBLEM SOLVING 375

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5 7 = 2 n Set the cross products equal to each other.
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35 = 2 n Multiply.
35
= n Divide 35 by 2, the number multiplied by n.
2
1
n = 17 or 17.5 Simplify.
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4. INTERPRET. Check your work.This result is reasonable since it is between 15
and 20 miles. State your conclusion: 7 inches corresponds to 17.5 miles.

Work Practice 1

We can also solve Example 1 by writing the proportion
2 inches 7 inches
=
5 miles n miles
Although other proportions may be used to solve Example 1, we will solve by
writing proportions so that the numerators have the same unit measures and the
denominators have the same unit measures.

Example 2 Finding Medicine Dosage PRACTICE 2
An auto mechanic recommends
The standard dose of an antibiotic is 4 cc (cubic centimeters) for every 25 pounds
that 3 ounces of isopropyl
(lb) of body weight.At this rate, find the standard dose for a 140-lb woman.
alcohol be mixed with a tankful
Solution: of gas (14 gallons) to increase
the octane of the gasoline for
1. UNDERSTAND. Read and reread the problem. You may want to draw a
better engine performance.
diagram to estimate a reasonable solution.
At this rate, how many gallons
of gas can be treated with a
140–pound woman
25 pounds 4 cc 16-ounce bottle of alcohol?
25 pounds 4 cc
25 pounds 4 cc
25 pounds 4 cc
25 pounds 4 cc
15 pounds ?
140 pounds over 20 cc

From the diagram, we can see that a reasonable solution is a little over 20 cc.
2. TRANSLATE.We will let n represent the unknown number. From the problem,
we know that 4 cc is to 25 pounds as n cc is to 140 pounds, or
cubic centimeters : 4 = n ; cubic centimeters
pounds : 25 140 ; pounds
3. SOLVE:

4 n
25 = 140 Answer
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2. 74 or 74.6 gal
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