Question

The length of a rectangle is 3 less than twice the width. Write a function rule for the perimeter in terms of w, the width

Answer 1

let's translate this word problem into math

the length (L) is (=) 3 less than (-3) twice the width (2*W).

L=-3+2W

we want to find the perimiter

the perimiter, P is P=2(L+W)

if we subsitute -3+2W for L from our first equation into our perimiter equation, we get

P=2(-3+2W+W)

P=2(-3+3W)

P=-6+6W

P=6W-6

so P(W)=6W-6 is the function of the perimiter in terms of the width

Answer 2

l = 2w-3

P = 2(l+w)

substitute in for l

P = 2(2w-3 +w)

combine like terms

P = 2(3w-3)

P = 6w-6

P(w) = 6(w-1)