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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol
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17 Dec 2022, 10:43
17 Dec 2022, 10:43
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Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
A. \(y + 3z\)
B. \(\frac{y +z}{4}\)
C. \(2y + 3z\)
D. \(3y + z\)
E. \(3y + 4.5z\)
A. \(y + 3z\)
B. \(\frac{y +z}{4}\)
C. \(2y + 3z\)
D. \(3y + z\)
E. \(3y + 4.5z\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Re: Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol
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19 Dec 2022, 09:25
19 Dec 2022, 09:25
1
Expert Reply
Milk concentration in mix would be \(1\%x+2\%y+3\%z\) and on the other hand we are told that in (x+y+z) there is 1.5% of milk. Hence:
\(1\%x+2\%y+3\%z=1.5\%(x+y+z)\);
\(x+2y+3z=1.5x+1.5y+1.5z\);
\(0.5x=0.5y+1.5z\);
\(x=y+3z\).
Answer: A
\(1\%x+2\%y+3\%z=1.5\%(x+y+z)\);
\(x+2y+3z=1.5x+1.5y+1.5z\);
\(0.5x=0.5y+1.5z\);
\(x=y+3z\).
Answer: A
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol
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02 Jan 2023, 13:12
02 Jan 2023, 13:12
GeminiHeat wrote:
Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
A. \(y + 3z\)
B. \(\frac{y +z}{4}\)
C. \(2y + 3z\)
D. \(3y + z\)
E. \(3y + 4.5z\)
A. \(y + 3z\)
B. \(\frac{y +z}{4}\)
C. \(2y + 3z\)
D. \(3y + z\)
E. \(3y + 4.5z\)
Let's start with a "word equation" and slowly turn it into an algebraic expression:
Total fat in mixture = 1.5% of (x+y+z)
(1% of x) + (2% of y) + (3% of z) = 0.015(x+y+z)
Rewrite as: 0.01x + 0.02y + 0.03z = 0.015x + 0.015y + 0.015z
Multiply both sides by 100: 1x + 2y + 3z = 1.5x + 1.5y + 1.5z
Rearrange and simplify: 0.5y + 1.5z = 0.5x
Multiply both sides by 2 to get: y + 3z = x
Answer: A
