Chapter 1.5, Problem 24E

a.

To determine

To calculate:

The literal equation in terms of $n$

Answer to Problem 24E

The formula in terms of $n$ is $\frac{d+2}{4}$ .

Explanation of Solution

Given information:

  $d=4n-2$

Calculation:

The given formula for penny size is:

  $d=4n-2$......................... (1)

Switch both sides as to get the formula for length of penny:

  $4n-2=d$

Add $2$ from both sides if equations:

  $\begin{array}{l}4n-2+2=d+2\\ 4n=d+2\end{array}$

Divide by $4$ :

  $\begin{array}{l}\frac{4}{4}n=\frac{d+2}{4}\\ n=\frac{d+2}{4}\end{array}$

b.

To determine

To calculate:

The length of penny for penny size $3,6$ and $10$

Answer to Problem 24E

The length of penny for penny size $3,6$ and $10$ is $\frac{5}{4},2$ and $3$ respectively.

Explanation of Solution

Given information:

  $\begin{array}{l}{d}_1=3\\ d_2=6\\ d_3=10\end{array}$

Calculation:

From the subpart (a):

The formula for length of penny is derived as:

  $n=\frac{d+2}{4}$

Put the given data:

  $\begin{array}{l}{n}_1=\frac{d_1+2}{4}=\frac{3+2}{4}=\frac{5}{4}\\ n_2=\frac{d_2+2}{4}=\frac{6+2}{4}=2\\ n_3=\frac{d_1+2}{4}==\frac{10+2}{4}=3\end{array}$