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. n= Question 2 b. Use the equation from part (a) to find the lengths of nails with the following penny sizes: 3, 6, and 10. A 3-penny nail is inches. A 6-penny nail is inches. A 10-penny nail is inches.

Answer 1

d=4n-2, d+2=4n-2+2, d+2=4n
(d+2)/4=(4n)/4, 1/4d+1/2=n
n=1/4n+1/2

size 3=
n=1/4*3/1=3/4, 3/4+1/2=5/4=1 1/4
size 3=1 1/4

size 6=
n=1/4*6/1=6/4, 6/4+1/2=8/4=2
size 6=2

size 10=
n=1/4*10/1=10/4, 10/4+1/2=12/4=3
size 10=3

Answer 2

The penny size d is given by the literal equation
`d=4n-2`

Where n is the length (in inches) of the nail.

We can deduce the value of n from equation above:

`(d+2)/4=n`

Now we have to find n with various values of d.

1. when d = 3 inches

`n=(3+2)/4`

`=>n=5/4`

n = 1.25 inches

2. when d = 6 inches

`n=(6+2)/4`

`=>n=8/4`

n = 2 inches

3. when d = 10 inches

`n=(10+2)/4`

`=>n=12/4`

n = 3 inches