Problem Solving

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) y + z/4

C) 2y + 3z

D) 3y + z

E) 3y + 4.5z

Solution:

We are given that 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. We can use this information to create the following equation:

0.01x + 0.02y + 0.03z = 0.015(x + y + z)

Multiply the entire equation by 1000, we have:

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

We must now get x in terms of y and z:

5y + 15z = 5x

We can divide the entire equation by 5:

y + 3z = x

Answer:A

Hi Srishti_15,

This is an "in terms of" question; these questions are usually built around 4-5 algebra steps and are fairly straight-forward "math" questions.

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

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