Question

Drag each tile to the correct box.  Not all tiles will be used.

Chris plans to mulch the border surrounding a rectangular garden in his backyard. If the length, l, of the garden (excluding its border) is 3 more than twice its width, w, and the width of the border is 1/4 w, which function represents the area, A, to be mulched in terms of w?

Answer 1

Step 1:

width of the garden: w

length of the garden: 2w+3

Step 2:

width of the entire plot: w+0.5w=1.5w

length of the entire plot: (2w+3) + 0.5w = 2.5w+3

Step 3:

area of the garden: w(2w+3)

area of the entire plot: 1.5w(2.5w+3)

Step 4:

area of the garden: 2w^2+3w

area of the entire plot: 3.75w^2+4.5w

Step 5:

area of border= area of the entire plot - area of the garden

area of border= 3.75w^2+4.5w - (2w^2+3w)

Step 6:

area of border= 3.75w^2+4.5w - 2w^2 - 3w

Step 7:

area of border= 1.75w^2+1.5w

Answer 2

Step 1:
width of the garden: w
length of the garden: 2w+3
Step 2:
width of the entire plot: w+0.5w=1.5w
length of the entire plot: (2w+3) + 0.5w = 2.5w+3
Step 3:
area of the garden: w(2w+3)
area of the entire plot: 1.5w(2.5w+3)
Step 4:
area of the garden: 2w^2+3w
area of the entire plot: 3.75w^2+4.5w
Step 5:
area of border= area of the entire plot - area of the garden
area of border= 3.75w^2+4.5w - (2w^2+3w)
Step 6:
area of border= 3.75w^2+4.5w - 2w^2 - 3w
Step 7:
area of border= 1.75w^2+1.5w