A construction worker is building a wall. The wall is

20

yd

long. He needs to place a stud every

16

in

. The first stud has already been placed at one end of the wall. How many additional studs are needed, if the last stud will be placed at the other end of the wall? First fill in the blanks on the left side using the ratios shown.

I believe it is 45 studs to the end of the wall

Step-by-step explanation:

First, convert 20 yds to 60 ft. and then from 60 ft to 720 in.

Use the formula for the nth term of an arithmetic sequence:

l = a + (n-1) d:

Here l = 720 ft, and a = 0. The common difference, d, is 16 in. Our task is to determine how many studs are needed.

Substituting the knowns, we get 720 = 0 + (n - 1) (16), which simplifies to:

720 = (n-1) (16).

Divide both sides by 16 to isolate (n-1) : 45 = n - 1.

Adding 1 to both sides results in 46 = n.

46 studs total are needed; if the worker has already placed the first stud, then 45 additional studs are needed.