6th Edition

ISBN: 9781285074672

Author: Larson

Publisher: CENGAGE L

Concept explainers

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Videos

Question

Chapter 1.1, Problem 51E

To determine

To complete the table which is provided in the question.

Expert Solution

Answer to Problem 51E

The complete table is obtained as:

DVDs	Cost (dollars)	Amount left (dollars)
1	1⋅4=4	200−4=196
2	2⋅4=8	200−8=192
3	3⋅4=12	200−12=188
4	4⋅4=16	200−16=184

Explanation of Solution

Given information:

The total yearly rental budget is $200 and each rental cost is $4.

Calculation:

From, the table, it can be observed that in Cost (dollars) column, total rental cost is written which is a product of number of DVDs and rental cost of each DVD and Amount left (dollars) column is obtained by subtracting the cost of DVDs from $200.

Hence, the complete table is obtained as:

DVDs	Cost (dollars)	Amount left (dollars)
1	1⋅4=4	200−4=196
2	2⋅4=8	200−8=192
3	3⋅4=12	200−12=188
4	4⋅4=16	200−16=184

To determine

To write the variable expression for cost of r rentals.

Expert Solution

Answer to Problem 51E

The variable expression for cost of r rentals is obtained as:

C=4⋅r

Explanation of Solution

Given information:

The total yearly rental budget is $200 and each rental cost is $4.

Calculation:

From, the table, it can be observed that in Cost (dollars) column, total rental costC is written which is a product of number of DVDs, r and rental cost of each DVD that is $4.

Hence,

The variable expression for cost of r rentals is obtained as:

C=4⋅r

To determine

To write the variable expression for amount of the budget left after r rentals.

Expert Solution

Answer to Problem 51E

The variable expression is obtained as:

A=200−4⋅r

Explanation of Solution

Given information:

The total yearly rental budget is $200 and each rental cost is $4.

Calculation:

From, the table, it can be observed that in Cost (dollars) column, Amount left (dollars) column is obtained by subtracting the total cost of DVDs, C from $200.

Total cost is obtained as:

C=4⋅r

Hence,

The variable expression is obtained as:

A=200−CA=200−4⋅r

To determine

Determine the number of DVD which can be rented before the $200 is spent.

Expert Solution

Answer to Problem 51E

The number of DVD which can be rented before the $200 is spent is 50.

Explanation of Solution

Given information:

The total yearly rental budget is $200 and each rental cost is $4.

Calculation:

Therefore,

The variable expression for cost of r rentals is obtained as:

C=4⋅r

Since, C=200 as $200 is spent. Then r gives the total number of DVDs which can be rented before $200 is spent.

So,

r=2004r=50

Hence,

The number of DVD which can be rented before the $200 is spent is 50.

Chapter 1.1, Problem 50E

Chapter 1.1, Problem 52E

Chapter 1 Solutions

ELEMENTARY+INTERMEDIATE ALGEBRA

Ch. 1.1 - Prob. 1C Ch. 1.1 - Prob. 2C Ch. 1.1 - Prob. 3C Ch. 1.1 - Prob. 4C Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E

Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - 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