Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is $12$ feet long, and each strand of his Christmas lights will wrap around a $70$ -inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing? $\newline$ A) $6$ $\newline$ B) $7$ $\newline$ C) $8$ $\newline$ D) $9$

Full solution

Q. Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is

12

feet long, and each strand of his Christmas lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

\newline

6

\newline

7

\newline

8

\newline

9

Calculate total length: First, we need to calculate the total length of the railing that Kris needs to wrap with Christmas lights. Since the porch is square and has three sides to be wrapped, we multiply the length of one side by three. $\newline$ Calculation: $12$ \text{ feet per side} \times $3$ \text{ sides} = $36$ \text{ feet total}.
Convert to inches: Next, we need to convert the total length of the railing from feet to inches because the length of the Christmas light strand is given in inches. There are $12$ inches in a foot.$\newline$Calculation: $36$ \text{ feet} \times $12$ \text{ inches/foot} = $432$ \text{ inches}.
Determine number of strands: Now, we need to determine how many $70$ -inch strands of Christmas lights are required to cover $432$ inches of railing. We do this by dividing the total railing length by the length of one strand of lights. $\newline$ Calculation: $\frac{432 \text{ inches}}{70 \text{ inches per strand}} = 6.1714$ strands.
Round up to whole strands: Since Kris cannot use a fraction of a strand, he will need to use whole strands. Therefore, we round up the number of strands needed to the next whole number. $\newline$ Calculation: Kris needs $7$ strands because you can't have a fraction of a strand and $6$ strands would not be enough to cover the entire railing.