Chapter 6.4, Problem 21E

a.

To determine

To find: If it is legal to make a reproduction.

Answer to Problem 21E

It is legal to make the reproduction.

Explanation of Solution

Given information: It is illegal to reproduce a genuine U.S. bill except according to the following rule: Every side length of the reproduction must be less than $\frac{3}{4}$ times, or grater than $1\frac{1}{2}$ times, the corresponding side length of a genuine bill. Genuine bills are $6.14$ inches long and $2.61$ inches wide.

A given reproduction is $9.41$ inches long, and $4$ inches wide.

Calculation: Since, The length of reproduction is $\langle 6.14\times \frac{3}{4}=4.605$ or $\rangle 6.14\times \frac{3}{2}=9.21$ .

And The width of the reproduction is $\langle 2.61\times \frac{3}{4}=1.9575$ or $\rangle 2.61\times \frac{3}{2}=3.915$

Therefore, The given reproduction length is grater than $1\frac{1}{2}$ times of genuine bill.

The given reproduction width is grater than $1\frac{1}{2}$ times of genuine bill.

Hence, It is legal to make the reproduction.

b.

To determine

To find: If it is legal to make a reproduction.

Answer to Problem 21E

It is legal to make the reproduction.

Explanation of Solution

Given information: It is illegal to reproduce a genuine U.S. bill except according to the following rule: Every side length of the reproduction must be less than $\frac{3}{4}$ times, or grater than $1\frac{1}{2}$ times, the corresponding side length of a genuine bill. Genuine bills are $6.14$ inches long and $2.61$ inches wide.

A given reproduction is $4$ inches long, and $1.7$ inches wide.

Calculation: Since, The length of reproduction is $\langle 6.14\times \frac{3}{4}=4.605$ or $\rangle 6.14\times \frac{3}{2}=9.21$ .

And The width of the reproduction is $\langle 2.61\times \frac{3}{4}=1.9575$ or $\rangle 2.61\times \frac{3}{2}=3.915$

Therefore, The given reproduction length is less than $\frac{3}{4}$ times of genuine bill.

The given reproduction width is less than $1\frac{1}{2}$ times of genuine bill.

Hence, It is legal to make the reproduction.

c.

To determine

To find: If it is similar to a genuine U.S. bill.

Answer to Problem 21E

It is legal to make the reproduction.

Explanation of Solution

Given information: It is illegal to reproduce a genuine U.S. bill except according to the following rule: Every side length of the reproduction must be less than $\frac{3}{4}$ times, or grater than $1\frac{1}{2}$ times, the corresponding side length of a genuine bill. Genuine bills are $6.14$ inches long and $2.61$ inches wide.

A given reproduction is $24$ inches long, and $9$ inches wide.

Calculation: Since, The length of reproduction is $\langle 6.14\times \frac{3}{4}=4.605$ or $\rangle 6.14\times \frac{3}{2}=9.21$ .

And The width of the reproduction is $\langle 2.61\times \frac{3}{4}=1.9575$ or $\rangle 2.61\times \frac{3}{2}=3.915$

Therefore, The given reproduction length is grater than $1\frac{1}{2}$ times of genuine bill.

The given reproduction width is grater than $1\frac{1}{2}$ times of genuine bill.

Hence, It is legal to make the reproduction.