Algebra 2 variable equations

Question

the length of a small box is three more than four times the width. the perimeter of the box is 21 centimeters. what’s the length and width of the box

Answer 1

Hi,

length = L and width = W

This expression "the length of a small box is three more than four times the width" is L = 3 + 4W

on the other word, perimeter is 21 that means: 2L + 2W = 21

Now, replace L = 3 + 4W in an equation of perimeter

2L + 2W = 21 =====> 2 ( 3 + 4W ) + 2W = 21 =====> after distribute you have

10W = 15 ======> w = 1.5 and one more time use of L = 3 + 4W by plug in

w = 1.5

L = 3 + 4(1.5) = 9

W = 1.5 L = 9 centimeter

I hope it is useful,

Minoo

Answer 2

If you mean a rectangle, then let "w" represent the width of the rectangle. Then the length is 4w + 3.

The perimeter is all the way around the outside so:

w + (4w + 3) + w + (4w + 3) = 21

10w + 6 = 21

10w = 15

w = 15/10

w = 1.5

So the width is 1.5 cm

To find the length, use length = 4w + 3 = 4(1,5) + 3 = 6 + 3 = 9 cm