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The table below shows the ratios of black paint to white paint needed to make different shades of gray paint.


Shades of Gray Black: White
Gray Pearl 1:20
Urban Gray 1:16
Gray Fox 2:1
Volcanic Gray 8:1
If the paint company mixes 4 gallons of black paint with

gallon of white paint, which shade of gray will it make?

1 answer

To determine which shade of gray the paint company will make by mixing 4 gallons of black paint with white paint, we first need to express the amounts of black and white paint in the required ratio format.

Given:

  • Black paint: 4 gallons
  • White paint: \( x \) gallons

We will analyze the ratios of black paint to white paint for each of the shades of gray:

  1. Gray Pearl: 1:20

    • This means for every 1 part black, there are 20 parts white.
    • Ratio of black to white is \( \frac{1}{20} \).

  2. Urban Gray: 1:16

    • This means for every 1 part black, there are 16 parts white.
    • Ratio of black to white is \( \frac{1}{16} \).

  3. Gray Fox: 2:1

    • This means for every 2 parts black, there is 1 part white.
    • Ratio of black to white is \( \frac{2}{1} \) or 2.

  4. Volcanic Gray: 8:1

    • This means for every 8 parts black, there is 1 part white.
    • Ratio of black to white is \( \frac{8}{1} \) or 8.

Now, we need to find the amount of white paint needed to match the total number of blacks at the same ratio. This can be done by setting up equations based on the ratios.

Let’s examine these one by one:

  1. Gray Pearl (1:20) \[ \frac{4}{x} = \frac{1}{20} \Rightarrow x = 4 \times 20 = 80 \text{ gallons} \]

  2. Urban Gray (1:16) \[ \frac{4}{x} = \frac{1}{16} \Rightarrow x = 4 \times 16 = 64 \text{ gallons} \]

  3. Gray Fox (2:1) \[ \frac{4}{x} = \frac{2}{1} \Rightarrow 4 = 2x \Rightarrow x = \frac{4}{2} = 2 \text{ gallons} \]

  4. Volcanic Gray (8:1) \[ \frac{4}{x} = \frac{8}{1} \Rightarrow 4 = 8x \Rightarrow x = \frac{4}{8} = 0.5 \text{ gallons} \]

Now we compare the amount of white paint we have available (not specified, but based on our calculations):

Since the company is using 4 gallons of black paint and does not give the amount of white paint, we can find potential shades based on how much white paint would be appropriate:

  • Gray Pearl and Urban Gray produce much more than generally feasible white amounts (80 and 64 gallons).
  • Gray Fox fits at 2 gallons (ratio confirms it's much darker).
  • Volcanic Gray fits with only 0.5 gallons of white, making it a darker gray.

Thus, with 4 gallons of black paint, the ratio that is feasible with little or indeed less white paint is Volcanic Gray.

Therefore, the paint company makes Volcanic Gray with the given mixture.