Question

The penny size of a nail indicates the length of the nail. The penny size d is given by the literal equation d=4n-2, where n is the length (in inches) of the nail.A) Solve the equation for n.B) use the equation from part a) to find the length of nails with the following penny sizes: 3, 6, and 10.

Answer 1

Given: The penny size d is given by the equation

$d=4n-2$

where n is the length of the nail.

Required: a) To solve the equation for n

b) To use the equation to find out the length of the nail with the following penny sizes: 3, 6, and 10.

Explanation: The given equation can be solved for n as follows

$\begin{gathered} d-4n=-2 \\ -4n=-2-d \\ 4n=2+d \\ n=\frac{2+d}{4} \end{gathered}$

Now putting the value of d=3 we get

$\begin{gathered} n=\frac{2+3}{4} \\ n=\frac{5}{4} \end{gathered}$

Again putting d=6 we get

$n=\frac{2+6}{4}$$\begin{gathered} n=\frac{8}{4} \\ n=2 \end{gathered}$

Finally putting d=10 we get

$\begin{gathered} n=\frac{2+10}{4} \\ n=3 \end{gathered}$

Final Answer: a) The equation for n is

$n=\frac{2+d}{4}$

b) The length of the nail with penny sizes 3,6, and 10 is 5/4, 2, and 3 respectively.