lachlanc wrote:Three grades of milk are 1%, 2% and 3% fat by vloume. If x gallons of the 1% grade, y gallons of the 2% grade and z gallons of the 3% grade are combined to create x+y+z gallons of a 1.5% grade, what is x in terms of y and z?

A) y + 3z
B) (y+z) / 4
C) 2y + 3z
D) 3y + 2z
E) 3y + 4.5z

OA: A

Please discuss

This is a mixture problem:

% 1 fat by volume means: 1 UNIT FAT/100 UNITS MILK

so lets say you mix 50 mls of 1 % and 50 mls of 2 % milk

from the first solution you will get 0.5 ml of fat ( 1 % of 50)
from the second solution you will get 1 ml of fat ( 2 % of 50)

now you have 1.5 ml of fat and 100 ml milk

so you new fat percent is 1.5 ml / 100 ml = 1.5 %

if we formulate this:

a % X + b % Y = c % ( X+Y)

Going back to our problem:

1 x + 2 y + 3 z = 1.5 (x+y+z)

x + 2y + 3z = 1.5x+1.5y+1.5z

x = y+3z

lachlanc wrote:Three grades of milk are 1%, 2% and 3% fat by vloume. If x gallons of the 1% grade, y gallons of the 2% grade and z gallons of the 3% grade are combined to create x+y+z gallons of a 1.5% grade, what is x in terms of y and z?

A) y + 3z
B) (y+z) / 4
C) 2y + 3z
D) 3y + 2z
E) 3y + 4.5z

OA: A

Please discuss

the way i solved this one was to formulate it like an algebra problem

(1x+2y+3z)/(x+y+z)=1.5

1.5x+1.5y+1.5z = (1x+2y+3z)

.5x=.5y+1.5z
multiply both sides by 2

x=y+3z

lachlanc wrote:Three grades of milk are 1%, 2% and 3% fat by vloume. If x gallons of the 1% grade, y gallons of the 2% grade and z gallons of the 3% grade are combined to create x+y+z gallons of a 1.5% grade, what is x in terms of y and z?

A) y + 3z
B) (y+z) / 4
C) 2y + 3z
D) 3y + 2z
E) 3y + 4.5z

OA: A

Please discuss

the way i solved this one was to formulate it like an algebra problem

(1x+2y+3z)/(x+y+z)=1.5

1.5x+1.5y+1.5z = (1x+2y+3z)

.5x=.5y+1.5z
multiply both sides by 2

x=y+3z