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Three grades of milk are 1 percent, 2 percent and 3 percent

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

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New post 29 Jan 2014, 15:33
I solved this by using differentials

1% - x
2% - y
3% - z

So then x+y+z is also given as 1.5%, which is in fact the weighted average

Let's just play with nice numbers here

10% - x
20% - y
30% - z

x + y + z = 15%

So -5x+5y+15z = 0

X = Y + 3Z

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

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New post 26 Oct 2014, 10:13
Bunuel - Where can I find challenging mixture problems/weighted avg problems to practice? Can you please help?

Thanks.
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent  [#permalink]

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New post 27 Oct 2014, 06:20
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p2bhokie wrote:
Bunuel - Where can I find challenging mixture problems/weighted avg problems to practice? Can you please help?

Thanks.


Check our Questions Bank: viewforumtags.php

Mixture problems made easy: mixture-problems-made-easy-49897.html

All DS Mixture Problems to practice: search.php?search_id=tag&tag_id=43
All PS Mixture Problems to practice: search.php?search_id=tag&tag_id=114

GMAT PS Question Directory by Topic & Difficulty: gmat-ps-question-directory-by-topic-difficulty-127957.html
GMAT DS Question Directory by Topic & Difficulty: ds-question-directory-by-topic-difficulty-128728.html

Hope this helps.
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent  [#permalink]

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New post 29 Aug 2016, 10:17
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. (y +z) / 4
C. 2y + 3z
D. 3y + z
E. 3y + 4.5z


Please find the solution as attached
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent  [#permalink]

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New post 25 Jun 2017, 18:00
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. (y +z) / 4
C. 2y + 3z
D. 3y + z
E. 3y + 4.5z


x + 2y + 3z = 1.5(x+y+z)

x + 2y + 3z = 1.5x + 1.5y + 1.5z

x + 0.5y + 1.5z = 1.5x

0.5y + 1.5z = 0.5x

y + 3z = x
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent  [#permalink]

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New post 24 Nov 2017, 12:46
I tried to solve the problem with numbers.. can someone point out what's wrong with my logic?

400 gallons of X = 4 grams of fat
100 gallons of Y = 2 grams of fat
100 gallons of Z = 3 grams of fat

4+2+3 / 400+100+100 = 1.5% fat

So answer choices A and D work for me??
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Three grades of milk are 1 percent, 2 percent and 3 percent  [#permalink]

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New post 24 Nov 2017, 13:51
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. \(3y + 4.5z\)


\(\frac{x}{100} + \frac{2y}{100} + \frac{3z}{100} = \frac{15*(x + y + z)}{1000}\)
\(x + 2y + 3z = \frac{15*(x + y + z)}{10}\)
\(0.5y + 1.5z = 0.5x\)
\(y + 3z = x\)

Hence, the answer is A
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent  [#permalink]

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New post 24 Jun 2018, 20:39
Hi All,

This is an "in terms of" question; these questions are usually built around 4-5 algebra steps and are fairly straight-forward "math" questions. To start, we can translate the given information into the following equation:

[(.01X) + (.02Y) + (.03Z)] / (X + Y + Z) = .015

(.01X + .02Y + .03Z0 = (.015X + .015Y + .015Z)

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

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

And then combine like terms....

5Y+ 15Z = 5X

And then divide everything by 5...

Y + 3Z = X

Final Answer:

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

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New post 24 Nov 2018, 15:45
A video explanation can be found here:
https://www.youtube.com/watch?v=aXGmN6qg8Hg

In mixture problems we’ll typically see (1) some sort of a substance (in this case, milk) and (2) some characteristic of the substance (in this case, fat) as a fraction or (usually) a percentage of the volume of the substance.

If the volumes of our three types of milk are expressed as x, y, z:

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

x + 2y + 3z = 1.5(x + y + z)

2x + 4y + 6z = 3(x + y + z)

Then isolate x:

x = y + 3z
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Re: 3 grades of milk are 1 %, 2% and 3% by volume. If x gallons  [#permalink]

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New post 25 Sep 2019, 05:56
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Re: 3 grades of milk are 1 %, 2% and 3% by volume. If x gallons   [#permalink] 25 Sep 2019, 05:56

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