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

First write and solve an equation.

2(area of white paint) = area of black paint

What is the length of the hallway?

Sagot :

MrRoyal

The area of a shape is the amount of space it can occupy.

  • The same hallway be painted with the same pattern, but using twice as much black paint as white paint
  • The length of the hallway is 40 feet

From the complete question (see attachment), the length of the white area is:

[tex]\mathbf{Length = x + x + x + x + x}[/tex]

[tex]\mathbf{Length = 5x}[/tex]

The width is:

[tex]\mathbf{Width = 6}[/tex]

So, the area of the white segment is:

[tex]\mathbf{Area = Length \times Width}[/tex]

[tex]\mathbf{Area = 5x \times 6}[/tex]

[tex]\mathbf{Area = 30x }[/tex]

The length of the black area is:

[tex]\mathbf{Length = x + 1 + x + 1 + x+1 +x +1}[/tex]

[tex]\mathbf{Length = 4x + 4}[/tex]

The width is:

[tex]\mathbf{Width = 6}[/tex]

So, the area of the black segment is:

[tex]\mathbf{Area = Length \times Width}[/tex]

[tex]\mathbf{Area = (4x + 4) \times 6}[/tex]

[tex]\mathbf{Area = 24x + 24}[/tex]

So, their areas  are:

[tex]\mathbf{Area = 30x }[/tex] --- white area

[tex]\mathbf{Area = 24x + 24}[/tex] --- black area

The paints

The equation is given as:

[tex]\mathbf{2 \times White = Black}[/tex]

Substitute the areas

[tex]\mathbf{2 \times 30x = 24x + 24}[/tex]

[tex]\mathbf{60x = 24x + 24}[/tex]

Collect like terms

[tex]\mathbf{60x - 24x = 24}[/tex]

[tex]\mathbf{36x = 24}[/tex]

Divide both sides by 36

[tex]\mathbf{x = \frac 23}[/tex]

Because x has a positive real value, then the same hallway be painted with the same pattern, but using twice as much black paint as white paint

Length of the hallway

To calculate the length of the hallway, we simply equate both areas;

[tex]\mathbf{30x = 24x + 24}[/tex]

Collect like terms

[tex]\mathbf{30x - 24x = 24}[/tex]

[tex]\mathbf{6x = 24}[/tex]

Divide both sides by 6

[tex]\mathbf{x = 4}[/tex]

So, the length of the hallway is the sum of the following lengths:

[tex]\mathbf{Length = 5x}[/tex]

[tex]\mathbf{Length = 4x + 4}[/tex]

So, we have:

[tex]\mathbf{Length =5x + 4x + 4}[/tex]

[tex]\mathbf{Length =9x + 4}[/tex]

Substitute 4 for x

[tex]\mathbf{Length =9 \times 4 + 4}[/tex]

[tex]\mathbf{Length =40}[/tex]

So, the length of the hallway is 40 feet

Read more about areas at

https://brainly.com/question/5688437

View image MrRoyal
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