Part A: What does the numerator of this rational expression represent?
ANSWER:
Numerator (200x-300) gives profit when x watches are sold.
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Part B: What does the denominator of this rational expression represent?
ANSWER:
Denominator (x) represents the number of watches sold.
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Part C: Rewrite the expression [tex]\frac{200x-300}{x}[/tex]
as a sum of two fractions, and simplify.
ANSWER:
[tex]\frac{200x-300}{x}[/tex]
[tex]=\frac{200x}{x}-\frac{300}{x}[/tex]
[tex]=200-\frac{300}{x}[/tex]
Hence simplified fraction form is [tex]200-\frac{300}{x}[/tex]
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Part D: What does each part in the expression from part C represent?
ANSWER:
First part is (200) which means maximum average prfit can be 200.
Second part [tex]-\frac{300}{x}[/tex]
is negative and number of watches (x) is in denominator so as the number of sold watches increases, then [tex]\frac{300}{x}[/tex]
decreases and due to negative sign, decrease in average profit value becomes less.
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Part E: Ryan also earns money by selling colored watch bands with the watches he sells. The linear expression 100x – 50 models Ryan’s additional income. What is the expression that models the new average profit, including the bands? Note: To obtain the new average profit expression, add the linear expression to the original rational expression. Write the new profit expression as one fraction.
ANSWER:
We just need to add both profit expressions:
[tex]\frac{200x-300}{x}+100x – 50[/tex]
[tex]=\frac{200x-300}{x}+\left(100x-50\right)\cdot\frac{x}{x}[/tex]
[tex]=\frac{200x-300}{x}+\frac{\left(100x^2-50x\right)}{x}[/tex]
[tex]=\frac{200x-300+100x^2-50x}{x}[/tex]
[tex]=\frac{100x^2+150x-300}{x}[/tex]
Hence final profit expression is [tex]\frac{100x^2+150x-300}{x}[/tex]
Answer:
Step-by-step explanation:
Given that Ryan has his own business selling watches, and he wants to monitor his profit per watch sold. The expression \frac{200x-300}{x} models the average profit per watch sold, where x is the number of watches sold.
Numerator = total profit for all x watches
Denominator = No of watches sold
C) [tex]\frac{200x-300}{x} =200-\frac{300}{x}[/tex]
D) 200 is the fixed profit irrespective of no of watches sold but second expression is 300/watches sold thus increases when x increases.
E) [tex] Additional Income = 100x-50[/tex]
New profit = [tex]\frac{200x-300}{x} +100x-50\\=\frac{100x^2+150x-300}{x}[/tex]
