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=(2+d)/(4) \end{gathered}`

Now putting the value of d=3 we get

`\begin{gathered} n=(2+3)/(4) \\ n=(5)/(4) \end{gathered}`

Again putting d=6 we get

`n=(2+6)/(4)`
`\begin{gathered} n=(8)/(4) \\ n=2 \end{gathered}`

Finally putting d=10 we get

`\begin{gathered} n=(2+10)/(4) \\ n=3 \end{gathered}`

Final Answer: a) The equation for n is

`n=(2+d)/(4)`

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