Question

a corrections officer is determining the number of bars needed to reinforce windows at an institution. uniform windows that are 2\frac{1}{2} feet wide need to have spacing at no more than \frac{1}{2} feet between bars. considering that the windows will also include bars at the left and right frames of the window, or essentially all the way across the windows, how many bars will be needed for each window? (you do not need to include the units. you only need to enter your answer as a number.)

Explanation:

Step1: Convert mixed - number to improper fraction

The width of the window is $2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$ feet.

Step2: Calculate the number of intervals

The maximum spacing between bars is $\frac{1}{2}$ feet. The number of intervals $n=\frac{\frac{5}{2}}{\frac{1}{2}}=\frac{5}{2}\times\frac{2}{1}=5$.

Step3: Calculate the number of bars

Since there are bars at both ends, the number of bars is one more than the number of intervals. So the number of bars $N=n + 1=5+1 = 6$.

Answer:

6