Need roofing help from expert math person

Question

I do metal roofing. The roof is 20 ft 4 inches wide.each roofing panel is 15 3/4 inches wide. How wide does the first and last panel have to be for them to be exact match on each side?

Answer 1

Hi Mike,

the nice thing about algebra is that you can do the math before doing the numbers. Here’s what I mean.

we need to use a number of full-width panels and two skinny panels. So

let w = number of whole panels

let s = width of a skinny panel

let t = total roof width in inches

so

roof is 20 ft 4 inches wide.each roofing panel is 15 3/4 inches

first, convert the full roof width to inches:

20 ft 4 inches = 20*12 +4 = 244 inches

so t = 244 inches

second, convert panel width to inches (as a fraction)

15 3/4 = (4 *15 + 3) / 4 = 63/4 inches

third, divide total width by panel width to get number of whole panels

244 / (63/4) = 4 *244 / 63 = 976 / 63 = 15.49

this means you will use 15 whole panels, and then cut another panel into the two skinny panels.

Now we get to use a formula:

t = w * 63/4 + 2*s

now solve for s

t - w* 63/4 = 2 s

(t - w*63/4)/2 = s

substitute for t and w

(244 - 15*63/4)/2 = s

put over common denominator: 4

(976/4 - 945/4)/2 = s

(31/4)/2 = s

31/8 = s

so each skinny panel is 31/8 inches wide = 3 7/8”