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sour milk

by B166418 » Sun Nov 25, 2012 8:28 am
Three grades of milk are 1 percent ,2 percent and 3 percent fat by volume .If x gallon of 1 percent grade ,Y gallon of 2 percent grade and z gallon of 3 percent grade are mixed to give x+Y+Z gallon of a 1.5 percent grade ,what is x in terms of y and z

y+3Z
y+Z/4
2Y+3Z
3Y+Z
3Y+4.5Z
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by Anindya Madhudor » Sun Nov 25, 2012 9:13 am
Given the information,
(0.01x + 0.02y + 0.03z) = 0.015(x+y+z)
=> x= y+3z
Last edited by Anindya Madhudor on Sun Nov 25, 2012 9:20 am, edited 1 time in total.
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by Anurag@Gurome » Sun Nov 25, 2012 9:13 am
B166418 wrote:Three grades of milk are 1 percent ,2 percent and 3 percent fat by volume .If x gallon of 1 percent grade ,Y gallon of 2 percent grade and z gallon of 3 percent grade are mixed to give x+Y+Z gallon of a 1.5 percent grade ,what is x in terms of y and z
Amount of fat in x gallons of 1% grade = x*(1/100) = x/100 gallons
Amount of fat in y gallons of 2% grade = y*(2/100) = (2y)/100 gallons
Amount of fat in z gallons of 3% grade = z*(3/100) = (3z)/100 gallons
Amount of fat in (x + y + z) gallons of 1.5% grade = (x + y + z)*(1.5/100) = [1.5*(x + y + z)]/100 gallons

Hence, x/100 + (2y)/100 + (3z)/100 = [1.5*(x + y + z)]/100
-----> x + 2y + 3z = 1.5x + 1.5y + 1.5z
-----> 1.5x - x = 2y - 1.5y + 3z - 1.5z
-----> 0.5x = 0.5y + 1.5z
-----> x = y + 3z

The correct answer is A
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