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 Q of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
Options:
A) 2
B) 2 1/2
C) 3
D) 3 1/2
E) 4
Given W:B = 3:5   That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.   But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,   1.5 : 2.5 gives  1.5 + 2.5= 
<gadget id="calculator"> 1.5 + 2.5</gadget>
<output>4</output>
4 gallons of mixture, but we want only 2 gallons, lets further reduce   0.75: 1.25 gives  1+1.5= 
<gadget id="calculator"> 1+1.5</gadget>
<output>2.5</output>
2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure   0.375: 0.625 gives  0.5 + 1= 
<gadget id="calculator"> 0.5 + 1</gadget>
<output>1.5</output>
1.5 gallons of mixture, thats less than 2 gallons of mixture Q, so not acceptable.   So correct ans is 2.5 gallons. 2 1/2
<result>B</result>
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 Q of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?