word problem algebra

Question

the length of a picture frame is 3in greater than the width. The perimeter is less than 52 in. Describe the dimension of the frame.

Answer 1

l = length call it x + 3

w = width call it x

perimeter = 2l + 2w therefore

52 = 2(x + 3) + 2(x)

52 = 2x + 6 + 2x

52 = 4x + 6, subtract 6

52 - 6 = 4x

46 = 4x, divide by 4

11.5 = x

width is 11.5

length is 14.5

check

52 = 2(14.5) + 2(11.5)

52 = 29 + 23

52 = 52

Hope it helps

Dennis

Answer 2

2(w+3)+ 2w < 52

2w + 6 + 2w < 52

4w +6 < 52

4w < 46

w < 46/4 = 23/2 = 11 + 1/2

L = 14 + 1/2

the width is less than 11 1/2

the length is less than 14 1/2

Answer 3

Draw a picture. Since the length is 3 greater then the width, we'll show the length as w + 3:

You can see that the perimeter would be w + w + 3 + w + w + 3 or 4w + 6 and since the perimeter is less than 52, we can say:

4w + 6 < 52

4w < 46

w < 11.5 and (of course), whatever the width is, the length is 3 more than that.