Math question (Just need some guidance on this problem)?

Question

As part of Black History Month in February, an artist is creating a mural on the side of a building. A painting of Dr. Martin Luther King Jr., will occupy the cent of the mural and will be surrounded by a border of uniform width showing other prominant African-Americans. The side of the building is 50 feet wide by 30 feet high, and the artist wants to devote 25% of the available space to the border. What should the width of the border be?

After looking at the back of the book, the answer should be 2.5 feet, however how do they come about this answer. And shouldn't you be trying to find the length of the border, not the width (murals are on one side of the building, it doesn't go off onto the two other walls it's touching)?

Any guidance on how they came about this answer?

I just typed the question as it was (asside from the few letters i missed, sorry ^^).

The only two answers i can come up with are, as you said, 12.5, and 7.5.

Answer 1

I got 12.5 feet, but maybe I did it wrong. Does it actually say that the WIDTH of the border is 50 feet? I took width to mean how how far one must walk to get from one side of the mural to the other.

You know that the total area is 1500 feet (30ftX50ft) and that 25% of 1500 is 375. That is the area of the border, so divide it by the length (30 ft) and it yields the width- 12.5 ft.

Answer 2

Assuming equal width of border all around,
let x = the width of the border:
(50 - 2x)(30 - 2x) = 3*30*50/4
1,500 - 160x + 4x^2 = 1,125
4x^2 - 160x + 375 = 0
4(x^2 - 40x) + 375 = 0
4(x^2 - 40x + 400) - 1600 + 375 = 0
4(x - 20)^2 - 1,225 = 0
(x - 20)^2 - 1,225/4 = 0
(x - 20 - 35/2) (x - 20 + 35/2) = 0
(x - 20 - 17.5) (x - 20 + 17.5) = 0
(x - 37.5) (x - 2.5) = 0
x = 37.5 or 2.5
Since x cannot equal 37.5,
x = 2.5 ft.

Answer 3

let the width be x feet
(50-2x)(30-2x)=(0.75)(30)(50)
1500-100x-60x+4x^2=1125
375-160x+4x^2=0
x=37.5 (rejected, too big) or x=2.5
x=2.5