A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?(A) 2(B) 2.5(C) 3(D) 3.5(E) 4

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LulP61906 LulP61906

28-10-2022
Mathematics

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A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?(A) 2(B) 2.5(C) 3(D) 3.5(E) 4

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EireneL765854 EireneL765854 · Answer 1 · 2022-10-28T21:25:53+02:00

3 parts whiite with 5 parts black = 8 parts in total

So, fractional white is:

[tex]\frac{3}{8}[/tex]

and, fractional black is:

[tex]\frac{5}{8}[/tex]

For 2 gallons, we need:

[tex]\begin{gathered} 2\cdot\frac{3}{8}=\frac{6}{8}=\frac{3}{4}=0.75\text{ gallons white} \\ \text{and} \\ 2\cdot\frac{5}{8}=\frac{10}{8}=\frac{5}{4}=1.25\text{ gallons black} \end{gathered}[/tex]

Remember, we can buy only 1 gallons and half gallon cans.

Thus,

• 0.75 gallons of white paint needed will be acquired from 1 gallon can.

,

• To get 1.25 gallons of black paint, we would need one 1 gallon can and one half-gallon can. Total of 1.5 gallons.

Thus, we need 1 + 1.5 = 2.5 gallons.

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Correct Answer

B

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