Question

A 6-foot-wide hallway is painted as shown, using equal amounts of white and black paint.

a. How long is the hallway?
b. Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint? Explain.

Answer 1

Thank you so much callculista

Explanation:

Answer 2

we know that

The hallway is painted using equal amounts of white and black paint

so

To know the amount of white paint------> calculate the area of white paint

`A=5x*6=30x\ ft^(2)`

To know the amount of black paint------> calculate the area of black paint

`A=(x+1)*4*6=(24+24x)\ ft^(2)`

equate the areas

`30x=(24+24x)\\30x-24x=24\\6x=24\\x=4\ ft`

Find the length of the hallway

`5x+(4x+4)=9x+4=9*4+4=40\ ft`

therefore

the answer part a) is

The hallway is
`40\ ft` long

Part b) Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint?

we know that

the amount of white paint is
`30x\ ft^(2)`

if the black paint is twice that the white paint

then

amount of black paint is
`2*30x=60x\ ft^(2)`

amount of black paint with the same pattern is
`(24+24x)\ ft^(2)`

equate

(24+24x)\ ft^{2}=(60x)\ ft^{2}

solve for the new value of x

`24x+24=60x\\ 60x-24x=24\\ x=24/36\\x= 2/3\ ft`

Find the new length of the hallway

`5x+(4x+4)=9x+4=9*(2/3)+4=10\ ft`

therefore

the answer is

Yes, the same hallway can be painted with the same pattern, using twice as much black paint as white paint, but the hallway decreases in length