Question

Abigail has a rectangular quilt with dimensions 36 inches by 48 inches. She Decides to sew a border on the quilt, so that the total area of the quilt is 1900 square inches. What will be the width of the border? Please Help!~

Answer 1

@mathmale Whenever u can, please help me. I have to go to school soon, so I might not be on, but if im not on may u please show it step by step (which you anyways do all the time :D) so that I understand it. Thanks!

Answer 2

And if anyone else can help me step by step that would be nice as well. Thanks to all! :)

Answer 3

Probably a simple question, but I tend to overthink things. XD

Answer 4

XD

Answer 5

Calculate the area of the quilt BEFORE border.
Add "w" to the dimensions of the quit and find the area of the quilt AFTER border. Set this result equal to 1900 square inches. Solve the resulting equation for the borer width, w.

Ask questions if these instructions are not sufficiently clear.

Answer 6

@mathmale 36w^2+48w=1900?

Answer 7

If that's (36+w)(48+w)=1900, yes! Otherwise, check your algebra.

Answer 8

Huh I am stuck. I don't understand what to do now. If I have (36+w)(48+w)=1900 would I add 36 and 48 then divide that number under 1900?

Answer 9

Your equation represents area = (length)(width) = 1900 .

You must multiply out (36+w)(48+w).

In the end you should have an equation arranged in standard form for a quadratic:

ax^2+bx+c=0

Answer 10

36x^2+48x+-1900=0?

Answer 11

Sorry for the delay, Mark. Note that your equation should be written in terms of "w," not in terms of "x," since we want to find the width, "w," of the border.

Try again. Multiply out (w+36)(w+48). Set your result = to 1900.

Answer 12

Your first term should be w^2, not 36x^2.

Answer 13

1728w^2+w=1900

1900/1728= (aproximately 1.1)

w=1.1

Answer 14

@mathmale may u check my math? Thx

Answer 15

Your first term should be just w^2.

Use the so-called "FOIL" method to multiply out (w+36)(w+48):

w^2 +48w +36w +1728

Remember, this is an AREA, and the actual area is 1900 square inches. You must solve for w.

Set w^2 +48w +36w +1728 equal to 1900 square inches.

Move that 1900 from the right side to the left side.

Combine 48w with 36w.

Your result?

Answer 16

w^2+84w+1728-1900=0

Answer 17

w^2+84w-172=0

Answer 18

This is a quadratic equation. How would you solve it for w?

Answer 19

w=2 and w=-86

but since -86 wont make any sense then I would only use w=2

Answer 20

I used quadratic equation

Answer 21

-b+/-(sqr)b^2-(4)(a)(c)/2a

Answer 22

Very good reasoning!!!

You should check your final answer (w=2 cm).

Do this by subst. "2cm" for w in (w+36)(w+48). Then find the product. If the product equals 1900 sq. cm, then you are correct!

Answer 23

YUP! :)

Answer 24

Thanks mathmale! :)

Answer 25

My great pleasure. So glad you've solved this problem!!

Answer 26

:)

Answer 27

Lol im doing this in my Principles of Engineering class. XD