EBK ALGEBRA 2
EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
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Concept explainers

Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Expert Solution & Answer
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Chapter 3.3, Problem 45PS
Solution

(a)

Use composition of functions to find the sale price of $85 worth of DVDs when the $15 discount is applied before the 10% discount.

  $63

Given:

An online movie store is having a sale. You decided to open a charge account and buy four DVDs.

  EBK ALGEBRA 2, Chapter 3.3, Problem 45PS , additional homework tip 1

Concept Used:

  • The composition function f∘g can be found by replacing x by gx in the function fx
  • The domain of a function y=fx is the set of all x values for which the function is defined.
  • A rational function y=fx is undefined for the values of x , for which the denominator is zero.
  • A radical function is defined for positive values greater than or equal to zero.
  • Zero product property: if a⋅b=0  then a=0 or b=0

Calculation:

According to given diagram

Sale price x = $85

For $15 discount: f(x) = x -15

For 10% discount: g(x) = x-0.1x

If the $15 discount is applied before the 10% discount.

  g(f(x))=g(f(85))                   =g(85−15)                   =g(70)                   =70−0.1(70)                   =70−7                   =63

So the sale price of $85 worth of DVDs when the $15 discount is applied before the 10% discount = $63.

(b)

Use composition of functions to find the sale price of $85 worth of DVDs when the 10% discount is applied before the $15 discount.

  61.5$

Given:

An online movie store is having a sale. You decided to open a charge account and buy four DVDs.

  EBK ALGEBRA 2, Chapter 3.3, Problem 45PS , additional homework tip 2

Concept Used:

  • The composition function f∘g can be found by replacing x by gx in the function fx
  • The domain of a function y=fx is the set of all x values for which the function is defined.
  • A rational function y=fx is undefined for the values of x , for which the denominator is zero.
  • A radical function is defined for positive values greater than or equal to zero.
  • Zero product property: if a⋅b=0  then a=0 or b=0

Calculation:

According to given diagram

Sale price x = $85

For $15 discount: f(x) = x -15

For 10% discount: g(x) = x-0.1x

If the 10% discount is applied before the $15 discount.

  f(g(x))=f(g(85))                   =f(85−0.1(85))                   =f(85−8.5)                   =f(76.5)                   =76.5−15                   =61.5

So the sale price of $85 worth of DVDs when the 10% discount is applied before the $15 discount = $61.5

(c)

Which order of discounts gives you a better deal? Explain.

The 10% discount is applied before the $15 discount.

Given:

An online movie store is having a sale. You decided to open a charge account and buy four DVDs.

  EBK ALGEBRA 2, Chapter 3.3, Problem 45PS , additional homework tip 3

Concept Used:

  • The composition function f∘g can be found by replacing x by gx in the function fx
  • The domain of a function y=fx is the set of all x values for which the function is defined.
  • A rational function y=fx is undefined for the values of x , for which the denominator is zero.
  • A radical function is defined for positive values greater than or equal to zero.
  • Zero product property: if a⋅b=0  then a=0 or b=0

Calculation:

If the $15 discount is applied before the 10% discount then the sale price of $85 worth of DVDs = $63.

If the 10% discount is applied before the $15 discount then the sale price of $85 worth of DVDs = $61.5

So we will get a better deal if the 10% discount is applied before the $15 discount.

i.e. $63-$61.5=$1.5 more discount.

So apply the 10% discount is applied before the $15 discount.

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Chapter 3.3, Problem 44PS
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Chapter 3.3, Problem 46PS

Chapter 3 Solutions

EBK ALGEBRA 2

Ch. 3.1 - Prob. 1GPCh. 3.1 - Prob. 2GPCh. 3.1 - Prob. 3GPCh. 3.1 - Prob. 4GPCh. 3.1 - Prob. 5GPCh. 3.1 - Prob. 6GPCh. 3.1 - Prob. 7GPCh. 3.1 - Prob. 8GPCh. 3.1 - Prob. 9GPCh. 3.1 - Prob. 10GP
Ch. 3.1 - Prob. 11GPCh. 3.1 - Prob. 12GPCh. 3.1 - Prob. 13GPCh. 3.1 - Prob. 14GPCh. 3.1 - Prob. 15GPCh. 3.1 - Prob. 16GPCh. 3.1 - Prob. 17GPCh. 3.1 - Prob. 18GPCh. 3.1 - Prob. 19GPCh. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60PSCh. 3.1 - Prob. 61PSCh. 3.1 - Prob. 62PSCh. 3.1 - Prob. 63PSCh. 3.1 - Prob. 64PSCh. 3.1 - Prob. 65PSCh. 3.1 - Prob. 66PSCh. 3.2 - Prob. 1GPCh. 3.2 - Prob. 2GPCh. 3.2 - Prob. 3GPCh. 3.2 - Prob. 4GPCh. 3.2 - Prob. 5GPCh. 3.2 - Prob. 6GPCh. 3.2 - Prob. 7GPCh. 3.2 - Prob. 8GPCh. 3.2 - Prob. 9GPCh. 3.2 - Prob. 10GPCh. 3.2 - Prob. 11GPCh. 3.2 - Prob. 12GPCh. 3.2 - Prob. 13GPCh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - 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Prob. 1DCCh. 3.3 - Prob. 2DCCh. 3.3 - Prob. 3DCCh. 3.4 - Prob. 1GPCh. 3.4 - Prob. 2GPCh. 3.4 - Prob. 3GPCh. 3.4 - Prob. 4GPCh. 3.4 - Prob. 5GPCh. 3.4 - Prob. 6GPCh. 3.4 - Prob. 7GPCh. 3.4 - Prob. 8GPCh. 3.4 - Prob. 9GPCh. 3.4 - Prob. 10GPCh. 3.4 - Prob. 11GPCh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46PSCh. 3.4 - Prob. 47PSCh. 3.4 - Prob. 48PSCh. 3.4 - Prob. 49PSCh. 3.4 - Prob. 50PSCh. 3.4 - Prob. 51PSCh. 3.4 - Prob. 1QCh. 3.4 - Prob. 2QCh. 3.4 - Prob. 3QCh. 3.4 - Prob. 4QCh. 3.4 - Prob. 5QCh. 3.4 - Prob. 6QCh. 3.4 - Prob. 7QCh. 3.4 - Prob. 8QCh. 3.4 - Prob. 9QCh. 3.4 - Prob. 10QCh. 3.4 - Prob. 11QCh. 3.4 - Prob. 12QCh. 3.4 - Prob. 13QCh. 3.4 - Prob. 14QCh. 3.4 - Prob. 15QCh. 3.4 - Prob. 16QCh. 3.4 - Prob. 17QCh. 3.4 - Prob. 18QCh. 3.4 - Prob. 19QCh. 3.5 - Prob. 1GPCh. 3.5 - Prob. 2GPCh. 3.5 - Prob. 3GPCh. 3.5 - Prob. 4GPCh. 3.5 - Prob. 5GPCh. 3.5 - Prob. 6GPCh. 3.5 - Prob. 7GPCh. 3.5 - Prob. 8GPCh. 3.5 - Prob. 9GPCh. 3.5 - Prob. 10GPCh. 3.5 - Prob. 11GPCh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - 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Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY