Three grades of milk are \(1\) percent, \(2\) percent, and \(3\) percent fat by volume. If \(x\) gallons of the \(1\) pe

[VJesus12]

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. \(\dfrac{y+z}4\)

C. \(2y+3z\)

D. \(3y+z\)

E. \(3y+4.5z\)

[spoiler]OA=A[/spoiler]

Source: GMAT Prep

[Brent@GMATPrepNow]

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. \(\dfrac{y+z}4\)

C. \(2y+3z\)

D. \(3y+z\)

E. \(3y+4.5z\)

[spoiler]OA=A[/spoiler]

Source: GMAT Prep

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

Cheers,
Brent