Questions: A construction worker is building a wall. The wall is 17.5 yd long. He needs to place a stud every 15 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 of the equation using three of the ratios shown. Then write your answer on the right side of the equation. ft yd mi (square)/(square) in stud × 5

A construction worker is building a wall. The wall is 17.5 yd long. He needs to place a stud every 15 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 of the equation using three of the ratios shown. Then write your answer on the right side of the equation.
ft yd mi
(square)/(square) in stud
× 5

Transcript text: A construction worker is building a wall. The wall is 17.5 yd long. He needs to place a stud every 15 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 of the equation using three of the ratios shown. Then write your answer on the right side of the equation. \begin{tabular}{|c|c|c|} \hline ft & yd & mi \\ \hline$\frac{\square}{\square}$ & in & stud \\ \hline$\times$ & 5 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Convert yards to feet

We are given the length of the wall in yards, but the stud spacing is in inches. So, we'll first convert yards to feet using the conversion factor 3 ft = 1 yd. Multiply 17.5 yd by (3 ft / 1 yd):

17.5 yd × (3 ft / 1 yd) = 52.5 ft

Step 2: Convert feet to inches

Now convert feet to inches using the conversion factor 12 in = 1 ft. Multiply 52.5 ft by (12 in / 1 ft):

52.5 ft × (12 in / 1 ft) = 630 in

Step 3: Calculate the number of studs

The studs are placed every 15 inches. Divide the total length in inches by the spacing between studs:

630 in / 15 in/stud = 42 studs

Since one stud has already been placed, subtract 1 to find the number of additional studs needed.