Can somebody please explain how my solutions manual got their answer, for the following problem? An artist intends to paint a 60 square foot mural, on a large wall that measures 18ft by 11ft. He plans to leave a uniform border, unpainted around it, on the wall. The illustration has 'w' standing for the white border around it. The solutions manual got 12 by 5 ft, for the mural. Can somebody explain how they got this?

Question

Can somebody please explain how my solutions manual got their answer, for the following problem? An artist intends to paint a 60 square foot mural, on a large wall that measures 18ft by 11ft.  He plans to leave a uniform border, unpainted around it, on the wall.  The illustration has 'w' standing for the white border around it.  The solutions manual got 12 by 5 ft, for the mural. Can somebody explain how they got this?

anonymous · Answer

if you go through the numbers that multiply to 60 (6x10, 5x12, 3x20), the only one that leaves you with equal space around the sides is 5x12. it's a logic-based answer. hope that helped.

anonymous · Answer

Not really...you see, I'm supposed to be coming up with an equation for the thing, then using the zero-factor property to factor it out...I've done the solutions manual equation and used the zero-factor property to factor it out...and I got what they got, from the equation...that being 23/3 or 3.  I just don't see how they got 12ft by 5ft from 23/3 and 3...

anonymous · Answer

F9

anonymous · Answer

F9?

anonymous · Answer

FINE ANS
NO EXPLANATION BY STEPS!!!!!!!!!!

anonymous · Answer

? There has to be an explanation...it's in the solutions manual..somehow they got from x =23/3 or x=3, to 12ft by 5ft.

anonymous · Answer

maybe 
$$(18-2x)(11-2x)=60$$

anonymous · Answer

Satellite73, that is the equation they used and I used...

anonymous · Answer

ok then why does that not give the answer?

anonymous · Answer

Because when you use the zero-factor property on that equation...

anonymous · Answer

multiply out and get 
$$4 x^2-58 x+138 = 0$$

anonymous · Answer

oooooooooooooooooh

anonymous · Answer

you don't get 12 by 5 ft...

anonymous · Answer

i see. you cannot use the "zero property" unless the thing is set to 0!

anonymous · Answer

which I did...

anonymous · Answer

you cannot use it in the form 
$$(18-2x)(11-2x)=60$$ you first have to write what i did

anonymous · Answer

I set the thing to 0, and got this equation...(18 - 2w)(11 - 2w) -60 = 0...

anonymous · Answer

now factor as 
$$2(x-3)(2x-23)=0$$ and now you can use the "zero property"

anonymous · Answer

I did factor it out as that..

anonymous · Answer

that is what they mean by "use the zero property".  then mean set = 0, then factor, then get your answer.  you have 
$$4x^2-58x+138=0$$ i would divide by 2 to get 
$$2x^2-28x+69=0$$ to make factoring easier.

anonymous · Answer

ok so your choice of answers are 
$$x=3$$ or 

$$x=\frac{23}{2}=11.5$$ and the second one is certainly not right.

anonymous · Answer

The solutions manual got x = 23/2 or x =3...then said that the answer to the problem is 12 by 5 ft.  It did not explain how it got from 23.2 or 3 to 12 by 5 ft...

anonymous · Answer

so the boarder is 3 feet yes?

anonymous · Answer

and if one dimension is 18 and you take away 3 from both sides you are left with 12

anonymous · Answer

the other dimension is 11 and you take away 3 from both sides you get 5

anonymous · Answer

?

anonymous · Answer

that is how they got the answer.  the solution 23/2 = 11.5 makes no sense in this case.

anonymous · Answer

An artist intends to paint a 60 square foot mural, on a large wall that measures 18ft by 11ft. 
we have found that the boarder is 3 feet yes?

anonymous · Answer

3 feet all around.  so you have a rectangle inside a rectangle.  the outer one is 18 by 11  
the inner one is 3 feet less on both sides, making it...