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Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol

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Math Expert
Joined: 02 Sep 2009
Posts: 61302
Re: Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol  [#permalink]

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15 Jan 2020, 09:07
gmatapprentice wrote:
Bunuel

Im not getting how you formulate the below equation. Would request if you can elaborate.
1%x+2%y+3%z=1.5%(x+y+z)1%x+2%y+3%z=1.5%(x+y+z)

It's a direct translation of the stem:

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?

x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed: 1%x+2%y+3%z
...to give x+y+z gallons of a 1.5 percent grade: 1.5%(x+y+z)
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol  [#permalink]

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17 Jan 2020, 06:42
Bunuel - thanks for the explanation.

Its basically the weighted average of the fat content correct?
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol  [#permalink]

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17 Jan 2020, 07:20
If z=0, then x MUST be equal to y in order to have 1.5% fat by volume. Let's test the choice

A. y + 3*0 = y (OK!)
B. (y+0) / 4 = y/4 (No!)
C. 2y + 3*0 = 2y (No!)
D. 3y + 0 = 3y (No!)
E. 3y + 4.5*0 = 3y (No!)

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Re: Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol  [#permalink]

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18 Jan 2020, 04:15
JimmyWorld 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. $$3y + 4.5z$$

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)

Multiplying the entire equation by 1000, we have:

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

We must now solve for x in terms of y and z:

5y + 15z = 5x

We can divide the entire equation by 5:

y + 3z = x

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Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol  [#permalink]

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18 Jan 2020, 07:59
- If y=0 and z=1, then x has to be 3 units (x:z=3:1) in order to have 1.5% fat by volume.
- If y=1 and z=0, then x has to be 1 units (x:y=1:1) in order to have 1.5% fat by volume.

Let's test the choice

A. y+3z= 0+3*1 = 3 (OK!)
y+3z= 1+3*0 = 1 (OK!)

We stopped here as we found certain final answer, which is (A)

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Three grades of milk are 1 percent, 2 percent and 3 percent fat by vol   [#permalink] 18 Jan 2020, 07:59

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