Weighted Avg/Mixture

Three grades of milk: 1%, 2%, and 3% fat by volume. X gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?
a. y + 3z
b. (y + z)/4
c. 2y + 3z
d. 3y + z
e. 3y + 4z

Here's one approach:

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

Hi jswesth,

This is an "in terms of" question; these questions are usually built around 4-5 algebra steps and are fairly straight-forward "math" questions. In most cases, it's actually rather difficult to TEST VALUES on these types of prompts.

First, translate the equation:

[(.01x) + (.02y) + (.03z)] / {x + y + z] = .015

.01x + .02y + .03z = .015x + .015y + .015z

Let's multiply everything by 1000 to get rid of the decimals....

10x + 20y + 30z = 15x + 15y + 15z

5y + 15z = 5x

y + 3z = x

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

I would actually pick simple values here.

If the total weighted average is a 1.5% grade, the easy thing to think of is equal parts 1% and 2%, but no 3%. So, say:
x = 1
y = 1
z = 0

If the question is asking for x in terms of y and z, then we want the answer choice that equals 1 when we plug in y = 1 and z = 0.

A. y + 3z --> 1 + 3(0) = 1 --> Success!

B. (y + z)/4 --> (1 + 0)/4 = 1/4 --> No.

C. 2y + 3z --> 2(1) + 3(0) = 2 --> No.

D. 3y + z --> 3(1) + 0 = 3 --> No.

E. 3y + 4z --> 3(1) + 4(0) = 3 --> No.

The answer is A.