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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mixture problem
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struggling_guy2001
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Black has to be 0,625% of the color (5/8)
White has to be 0,375% of the color (3/8)
So in a 2 gallon mixture we need 1,25 gallons of black and 0,75 gallos of white. To get 1,25 we need to buy 1,5 gallons of black, and for white we need only a gallon. 1+1,5=2,5.... B
White has to be 0,375% of the color (3/8)
So in a 2 gallon mixture we need 1,25 gallons of black and 0,75 gallos of white. To get 1,25 we need to buy 1,5 gallons of black, and for white we need only a gallon. 1+1,5=2,5.... B
IMO 2.5 gallons coz if 2 gallons of solution contains 3 parts of white and 5 parts of black paint then quantity of white and black paints in the mixture should be 3/4 gallons and 5/4 gallons respectively..arghya05 wrote: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
so for 3/4 gallon of white paint we need minimum a 1 gallon Can of white
and for 5/4 gallon of black paint we need minimum a 1 gallon Can of black and a half gallon Can of black.
So 1+1.5 = 2.5 gallons.. ans
Hence B.
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arghya05 wrote: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
We are given that a gray pain is obtained by mixing 3 parts of white paint with 5 parts of black paint. We are also given that the paint can be purchased in one or half gallon cans and that the total mixture is 2 gallons. We must determine the minimum number of gallons of paint needed.
Our given ratio is:
w/b = 3/5 = 1.5/2.5 = 0.75/1.25
As we can see, we need to have 0.75 gallons of white paint and 1.25 gallons of black paint in order to have 2 gallons of the mixed (i.e., gray) paint. However, in order to have the 0.75 gallons of white paint, we need to purchase 1 gallon of white paint, and in order to have the 1.25 gallons of black paint, we need to purchase 1.5 gallons of black paint. Thus, we need to purchase a total of 2.5 gallons of paint.
Answer: B
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