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 for a part a) to find lengths of nails with the following penny sizes: 3,6 and 10

Answer 1

Answer:

a) n = (d + 2)/4

b) when d = 3, n = 5/4

d = 6, n = 2

d = 10, n = 3

Step-by-step explanation:

Given:

The equation relating the penny size and the length of the nail:

`d=4n-2`

n = length of the nail

d = penny size

To find:

a) solve for n

b) using the equation in (a) to get the lengths of the nails with the following penny sizes: 3,6 and 10

a) We will make n the subject of the formula:

`\begin{gathered} d\text{ = 4n - 2} \\ add\text{ 2 to both sides:} \\ d\text{ + 2 = 4n} \\ \\ divide\text{ both sides by 4:} \\ n\text{ = }\frac{d\text{ + 2}}{4} \end{gathered}`

b) we need to find the values of n for d = 3, 6, and 10 respectively

when d = 3

`\begin{gathered} n\text{ = }\frac{3\text{ + 2}}{4} \\ n\text{ = 5/4} \end{gathered}`

when d = 6

`\begin{gathered} n\text{ = }\frac{6\text{ + 2}}{4} \\ n\text{ = 8/4 = 2} \end{gathered}`

when d = 10

`\begin{gathered} n\text{ = }(10+2)/(4) \\ n\text{ = 12/4 = 3} \end{gathered}`