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QuestionFind the length nn of a nail given its penny size d=4n−2d=4n-2. Also, determine nn for penny sizes 3, 6, and 10.

Studdy Solution

STEP 1

Assumptions1. The penny size dd of a nail is given by the equation d=4n−d =4n -, where nn is the length of the nail in inches. . We need to solve the equation for nn.
3. We need to find the lengths of nails with penny sizes3,6, and10.

STEP 2

First, we need to solve the equation d=4n−2d =4n -2 for nn. We can do this by isolating nn on one side of the equation.

STEP 3

Add2 to both sides of the equation to isolate the term nn.
d+2=nd +2 =n

STEP 4

Divide both sides of the equation by4 to solve for nn.
n=d+24n = \frac{d +2}{4}

STEP 5

Now that we have the equation for nn, we can find the lengths of nails with penny sizes3,, and10. We can do this by substituting the given penny sizes into the equation for nn.

STEP 6

Substitute d=3d =3 into the equation for nn.
n=3+24n = \frac{3 +2}{4}

STEP 7

Calculate the length of the nail with penny size3.
n=3+24=54=1.25 inchesn = \frac{3 +2}{4} = \frac{5}{4} =1.25\, inches

STEP 8

Substitute d=6d =6 into the equation for nn.
n=6+24n = \frac{6 +2}{4}

STEP 9

Calculate the length of the nail with penny size6.
n=6+24=84=2 inchesn = \frac{6 +2}{4} = \frac{8}{4} =2\, inches

STEP 10

Substitute d=10d =10 into the equation for nn.
n=10+24n = \frac{10 +2}{4}

STEP 11

Calculate the length of the nail with penny size10.
n=10+4=4=3 inchesn = \frac{10 +}{4} = \frac{}{4} =3\, inchesThe lengths of nails with penny sizes3,6, and10 are.25 inches, inches, and3 inches respectively.

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