Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.1 - Simplifying Rational Expressions - Exercise Set - Page 489: 8


a) \$350 b) \$260 c) The cost decreases when more machines are produced, as evidenced by the answers in (a) and (b)

Work Step by Step

a) In the equation, $x$ represents the number of fax machines and $C$ represents the cost per fax machine. Part (a) asks for the cost of 100 fax machines, so we plug 100 in for $x$: $\frac{250x+10000}{x} = \frac{250\cdot 100 + 10000}{100} = \frac{35000}{100} = 350$ b) We are now asked to find the cost for 1000 fax machines, so we substitute 1000 in for $x$: $\frac{250x+10000}{x} = \frac{250\cdot 1000 + 10000}{1000} = \frac{26000}{1000} = 260$ c) As the number of fax machines increases, the cost per fax machine decreases. We can see this by comparing parts (a) and (b) above. We can further see this when graphing the function and looking at the slope when $x>0$, and we see that the function decreases. This becomes more evident when we separate the fraction into two fractions: $C = \frac{250x}{x} + \frac{10000}{x}$. We can further simplify this into $C = 250 + \frac{10000}{x}$. If one fax machine is produced, $x=1$, so the cost is $250+\frac{10000}{1} = 250 + 10000 = 10250$. When more fax machines are produced, the fraction $\frac{10000}{x}$ results in a smaller number to add to $250$. For example, when 10000 fax machines are produced, the cost is $250+\frac{10000}{100000} = 250 + 1 = 251$.
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