Financial Algebra 1st Edition Chapter 2 Modeling a Business
Page 76 Problem 1 Answer
Given: Wholesale Price=x dollars
Retail Price=y dollars
To find: The markup amount
Solution:Wholesale price+Markup=Retail Price
x+Markup=y
Markup=y−x
The wholesale price of an item is x dollars and the retail price is y dollars, then the markup is y−x dollars
Page 77 Problem 2 Answer
Given: A banner company sells 5-foot banners to retailers for x dollars. The St. James Sign Shop marks them up90%
To find: Express the retail price at the St. James store
Solution: We will find the value of the markupThen find the retail price
Markup=90%of wholesale price
=90/100×x
=0.9x
Retail price=Wholesale price+Markup
=x+0.90x
=1.90x
A banner company sells 5 -foot banners to retailers for x dollars and the St. James Sign Shop marks them up90%, then the retail price will be1.90x
Page 77 Problem 3 Answer
If a widget has a low price, many people may want it and will be able to afford it, so a large quantity may be sold.If it has a high price, fewer widgets will be sold.
As the price increases, demand (the quantity consumers want) is likely to decrease, and as price decreases, demand increases.
The graph of the demand function has a negative slope. However, its curvature varies.
The demand function has a negative slope because as the price of a product increases the demand for the product will decrease.
Page 78 Problem 4 Answer
Here, we have to find the store’s markup. It’s given that an automobile GPS system is sold to stores at a wholesale price of $97
A popular store sells them for $179.99
Markup= Retail price−Wholesale price
= $179.99−$97=$82.99
So, the store’s markup is$82.99
Page 78 Problem 5 Answer
Here, we have to find the retail price of the CD rack. It’s given that a CD storage rack is sold to stores at a wholesale price of $18
Retail price=Markup+Wholesale price
=$13+$18=$82.99
So, the retail price of the CD rack is $82.99
Page 79 Problem 6 Answer
Here, we have to find the equation of the linear regression line.
Enter the ordered pairs(p is wholesale price and y is quantity demanded in hundreds) into your calculator.
Then use the statistics menu to calculate the linear regression equation.
The equation is of the form y=mx+b,where m is the slope and b is the y intercept.
Rounding the slope and y intercept to the nearest hundredth, the equation of the regression line is −136.08p+2,535.79
So, the equation of the linear regression line is q=−136.08p+2,535.79
Page 79 Problem 7 Answer
Here, we have to give the slope of the regression line and interpret the slope as a rate.
As the line is q=−136.08p+2,535.79
Comparing it with y=mx+c,where m is slope, q=mx+c=−136.08p+2,535.79,gives m=−136.08
The slope is −136.08.As a rate, the slope is expressed as garbage cans per dollar.
For each dollar increase in price, about 136 less garbage cans are demanded.
Page 79 Problem 8 Answer
Here, we have to find the correlation coefficient and interpret it.
Use a graphing calculator to find the correlation coefficient. Round r to the nearest hundredth r=−0.99.
As magnitude of r>0.75 hence strong correlation.
So, the correlation coefficient is r=−0.99, there is a strong negative correlation.
Page 79 Problem 9 Answer
Here, we have to find how many garbage cans would be demanded at a wholesale price of $18.00.
For demand of garbage bans of downloads put p=18
(do not forget that unit of q was in hundred)
q=−136.08×18+2,535.79
y=−2,449.44+2,535.79
86.35≈86
So, the garbage cans would be demanded at a wholesale price of $18.00 Is 86 hundred.
Page 79 Problem 10 Answer
Here, we have to determine whether our answer to part d is an example of extrapolation or interpolation and we have to explain.
In previous question the value of price was $18 which is out of the domain.
So, the answer to part d is an example of extrapolation,$18.00 is not in the domain.
Page 79 Problem 11 Answer
Here, we have to find how much money would the company receive from the garbage can sales. It’s given that
So, the money would the company receive from the garbage can sales is $154,800
Page 79 Exercise 1 Answer
Given that company that produces widgets has found its demand function to be q=−1,500p+90,000
For each dollar increase in the wholesale price we have to find how many fewer widgets are demanded
Now we have given the demand function as q=−1,500p+90,000
Now on substituing value of p as p+1
q=−1,500(p+1)+90,000
=−1,500p−90,000−1,500
=q−1500
Therefore we can say that 1500 widgets were demanded for each dollar increase in the wholesale price.
Hence the number of widgets demanded for each dollar increase in the wholesale price is 1500
Page 79 Exercise 2 Answer
Given that company that produces widgets has found its demand function to be q=−1,500p+90,000
For each dollar increase in the wholesale price we have to find how many fewer widgets are demanded
We have to find how many widgets would be demanded at a price of $20
We have given the demand equation as q=−1,500p+90,000
Now we have
q=−1,500×20+90,000
=−30,000+90,000
=60,000
Therefore the number of widgets demanded at a price of $20 is 60,000
Hence the number of widgets demanded at a price of $20 is 60,000.
Given that company that produces widgets has found its demand function to be q=−1,500p+90,000
For each dollar increase in the wholesale price we have to find how many fewer widgets are demanded
We have to find how many widgets would be demanded at a price of $21
We have given the demand equation as q=−1,500p+90,000
Now we have
q=−1,500×21+90,000
=−31,500+90,000
=58,500
Therefore the number of widgets demanded at a price of $21 is 58,500
Hence the number of widgets demanded at a price of $21 is58,500
Page 79 Exercise 4 Answer
Given that company that produces widgets has found its demand function to be q=−1,500p+90,000
For each dollar increase in the wholesale price we have to find how many fewer widgets are demanded
We have to find what is the difference in quantity demanded caused by the $1 increase in wholesale price.
Now we have given the demand function as q=−1,500p+90,000
Now on substituting value of p as p+1
q=−1,500(p+1)+90,000
=−1,500p−90,000−1,500
=q−1500
q−q′
=1500
Therefore the difference in quantity demanded caused by $1 increase in wholesale price is 1500
Hence the difference in quantity demanded caused by $1 increase in wholesale price is 1500
Page 79 Exercise 5 Answer
Given that company that produces widgets has found its demand function to be q=−1,500p+90,000
For each dollar increase in the wholesale price we have to find how many fewer widgets are demanded
We have to find how many widgets would be demanded at a price of $22.50
We have given the demand equation as q=−1,500p+90,000
Now we have
q=-1,500×22.5+90,000
=-33,750+90,000
=56,250
Therefore the number of widgets demanded at a price of $22.5 is 56,250
Hence the number of widgets demanded at a price of $22.5 is 56,250
Page 79 Exercise 6 Answer
Given that company that produces widgets has found its demand function to be q=−1,500p+90,000
For each dollar increase in the wholesale price we have to find how many fewer widgets are demanded
We have to find how much will all of the widgets cost the store to purchase at a price of $
Now we have the Number of widgets as
q=−1,500×22.5+90,000
=−33,750+90,000
=56,250
Now we have the cost as the product of price to the number of widegets that is
cost price=$22.50×56,250
=$1,265,625
So we have the cost to store all the widgets purchased at a price of $22.5 is $1,265,625
Hence we have the cost to store all the widgets purchased at a price of $22.5 is $1,265,625
Page 79 Exercise 7 Answer
Given that company that produces widgets has found its demand function to be q=−1,500p+90,000
store marks up the widgets that cost $22.50 at a rate of 50%,
We havr to to find the retail price of each widget.
Now we have the markup as the product of the cost with markup rate that is
Markup = $22.5×50%
=$22.5×0.5
=$11.25
Now we have the Retail price as the sum of markup to the wholesale price that is
Retail price =$22.5+$11.25
=$33.75
So we have the retail price as $33.75
Hence we have the retail price as $33.75
Chapter 2 Solving Linear Inequalities
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- Cengage Financial Algebra 1st Edition Chapter 2 Assessment Modeling a Business
- Cengage Financial Algebra 1st Edition Chapter 2 Exercise 2.1 Modeling a Business
- Cengage Financial Algebra 1st Edition Chapter 2 Exercise 2.2 Modeling a Business
- Cengage Financial Algebra 1st Edition Chapter 2 Exercise 2.4 Modeling a Business
- Cengage Financial Algebra 1st Edition Chapter 2 Exercise 2.5 Modeling a Business
- Cengage Financial Algebra 1st Edition Chapter 2 Exercise 2.6 Modeling a Business
- Cengage Financial Algebra 1st Edition Chapter 2 Exercise 2.7 Modeling a Business
- Cengage Financial Algebra 1st Edition Chapter 2 Exercise 2.8 Modeling a Business