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705-805 (Hard)|   Algebra|      
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sandra1122
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value Updated on: 06 Sep 2020, 02:00
Originally posted by sandra1122 on 08 Apr 2013, 04:25.
Last edited by Bunuel on 06 Sep 2020, 02:00, edited 2 times in total.
Renamed the topic and edited the question.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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59% (02:21) correct 41% (03:04) wrong based on 476 sessions

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If \(w=\frac{1+x\frac{y}{z^2}}{x+y}\), \(x=\frac{z}{2}\), and \(y=3\frac{z}{4}\),what is the value of w in terms of z?

A. 11/(10z)
B. 2z/5
C. 3z/10
D. 11z/10
E. 2z/5

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I tried to solve the problem several times, but still didn't get the OA.

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Bunuel
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 08 Apr 2013, 05:57
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If \(w=\frac{1+x\frac{y}{z^2}}{x+y}\), \(x=\frac{z}{2}\), and \(y=3\frac{z}{4}\),what is the value of w in terms of z?

A. 11z/10
B. 2z/5
C. 3z/10
D. 11z/10
E. 2z/5

I tried to solve the problem several times, but still didn't get the OA.
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Notice that options A and D are the same, as well as options B and E, so there are typos in answer choices.

In order A to be the correct answer it should read 11/(10z).

Say z=4, then \(x=\frac{z}{2}=2\), and \(y=3\frac{z}{4}=3\).

So, in this case we'd have that x=2, y=3 and z=4. Plug these values in the fraction to get w=11/40. Now, plug z=4 into the answer choices to see which one yields 11/40. Only A fits (assuming that there IS a typo and A actually must be 11/(10z)).

Hope it helps.
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value Updated on: 08 Apr 2013, 06:22
Originally posted by Zarrolou on 08 Apr 2013, 06:12.
Last edited by Zarrolou on 08 Apr 2013, 06:22, edited 1 time in total.
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Numerator : \(w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =\)
\(1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}\)
Denominator: \(\frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z\)
All together: \(\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}\)

Edited: Thanks Bunuel !
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 08 Apr 2013, 06:14
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Zarrolou
Numerator : \(w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =\)
\(1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}\)
Denominator: \(\frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z\)
All together: \(\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5}z=\frac{11}{10}z\)
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(11/8)/(5z/4)=11/(10z) not 11z/10.
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 08 Apr 2013, 06:20
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Bunuel
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Numerator : \(w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =\)
\(1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}\)
Denominator: \(\frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z\)
All together: \(\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5}z=\frac{11}{10}z\)

(11/8)/(5z/4)=11/(10z) not 11z/10.
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You're right. Typing mistake, I went MAD with all those [fraction][/fraction] Tags!
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sandra1122
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 08 Apr 2013, 18:23
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ok, 11/10z would fit the answer. Thanks guys.
But B and E aren't really typos, E is actually 2+z/5.
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 29 Oct 2015, 16:20
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Zarrolou
Numerator : \(w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =\)
\(1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}\)
Denominator: \(\frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z\)
All together: \(\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}\)

Edited: Thanks Bunuel !
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Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3\(\frac{z}{4}\) but then later you re-write this as \(\frac{3}{4}\)z

Isn't y a mixed number that should be \(\frac{12+z}{4}\)?
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 30 Oct 2015, 01:34
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Zarrolou
Numerator : \(w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =\)
\(1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}\)
Denominator: \(\frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z\)
All together: \(\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}\)

Edited: Thanks Bunuel !

Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3\(\frac{z}{4}\) but then later you re-write this as \(\frac{3}{4}\)z

Isn't y a mixed number that should be \(\frac{12+z}{4}\)?
Show more

It's not a mixed number, it's 3*z/4 and 3/4*z. So, both are the same (3z)/4.
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 30 Oct 2015, 03:34
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Zarrolou
Numerator : \(w=1+\frac{z}{2}*\frac{3}{4}z/z^2 =\)
\(1+\frac{z}{2}*\frac{3}{4}z*\frac{1}{z^2}=1+\frac{3}{8}=\frac{11}{8}\)
Denominator: \(\frac{z}{2}+\frac{3}{4}z=\frac{2z+3z}{4}=\frac{5}{4}z\)
All together: \(\frac{11}{8}/\frac{5z}{4}=\frac{11}{8}*\frac{4}{5z}=\frac{11}{10z}\)

Edited: Thanks Bunuel !

Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3\(\frac{z}{4}\) but then later you re-write this as \(\frac{3}{4}\)z

Isn't y a mixed number that should be \(\frac{12+z}{4}\)?

It's not a mixed number, it's 3*z/4 and 3/4*z. So, both are the same (3z)/4.
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Thank you Bunuel for your reply.

How do you know when it's a mixt number and when it is 3/4*z because to me they look the same?
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 30 Oct 2015, 05:17
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Hi Zarrolou,

Probably I'm asking a stupid question now, but I'm really confused.

In the OP it says that:
y=3\(\frac{z}{4}\) but then later you re-write this as \(\frac{3}{4}\)z

Isn't y a mixed number that should be \(\frac{12+z}{4}\)?

It's not a mixed number, it's 3*z/4 and 3/4*z. So, both are the same (3z)/4.

Thank you Bunuel for your reply.

How do you know when it's a mixt number and when it is 3/4*z because to me they look the same?
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If there is a variable involved it's always a multiplication (other case will be explicitly stated).
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If w=(1+x*y/z^2)(x+y), x=z/2, and y=3z/4, what is the value 14 Jan 2025, 22:24
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