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The quotient of x and y is 2. If x is 75% of z, which is
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Updated on: 09 Feb 2025, 13:22
Updated on: 09 Feb 2025, 13:22
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49% (02:31) correct
49% (02:59) wrong based on 14 sessions
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The quotient of x and y is 2. If x is 75% of z, which is \(\frac{3}{4}\) larger than w,, what is w in terms of y ?
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
Drill 2
Question: 7
Page: 498
Question: 7
Page: 498
Re: The quotient of x and y is 2. If x is 75% of z, which is
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18 Mar 2018, 07:28
18 Mar 2018, 07:28
1
Expert Reply
Explanation
Translate what you are told into algebra: \(\frac{x}{y}=2\) and \(x=\frac{75}{100}\times z=\frac{3}{4}\times z\).
Notice that the problem then tells you that z is larger than w, not z is of \(\frac{3}{4}\) w.
That means \(z=w+\frac{3}{4}w=(1+\frac{3}{4})w=\frac{7}{4}w\).
At this point, you can either Plug In or do algebra.
To Plug In, choose 4 for w, so z = 7, and \(x=\frac{3}{4}\times 7=\frac{21}{4}\).
If \(\frac{x}{y}=2\), then x = 2y, so \(\frac{21}{4}=2y\); \(y= \frac{21}{8}\).
Now plug \(\frac{21}{8}\) into the answer choices for y to see which hits your target number, w = 4.
Only choice (C) does. Alternatively, to do algebra, combine the first two equations you translated into algebra: \(2y=\frac{3}{4} z\); \(z=\frac{8}{3}\).
Combining this equation with the one you derived above, it follows that \(\frac{8}{3}y= \frac{7}{4}w\), and \(w= \frac{32}{21}y\); the answer is choice (C).
Translate what you are told into algebra: \(\frac{x}{y}=2\) and \(x=\frac{75}{100}\times z=\frac{3}{4}\times z\).
Notice that the problem then tells you that z is larger than w, not z is of \(\frac{3}{4}\) w.
That means \(z=w+\frac{3}{4}w=(1+\frac{3}{4})w=\frac{7}{4}w\).
At this point, you can either Plug In or do algebra.
To Plug In, choose 4 for w, so z = 7, and \(x=\frac{3}{4}\times 7=\frac{21}{4}\).
If \(\frac{x}{y}=2\), then x = 2y, so \(\frac{21}{4}=2y\); \(y= \frac{21}{8}\).
Now plug \(\frac{21}{8}\) into the answer choices for y to see which hits your target number, w = 4.
Only choice (C) does. Alternatively, to do algebra, combine the first two equations you translated into algebra: \(2y=\frac{3}{4} z\); \(z=\frac{8}{3}\).
Combining this equation with the one you derived above, it follows that \(\frac{8}{3}y= \frac{7}{4}w\), and \(w= \frac{32}{21}y\); the answer is choice (C).
Re: The quotient of x and y is 2. If x is 75% of z, which is
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19 Mar 2018, 19:06
19 Mar 2018, 19:06
sandy wrote:
The quotient of x and y is 2. If x is 75% of z, which is \(\frac{3}{4}y\)larger than w, what is w in terms of y ?
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
A. \(\frac{21}{32}y\)
B. \(\frac{20}{21}y\)
C. \(\frac{32}{21}y\)
D. \(\frac{32}{9}y\)
E. \(\frac{21}{8}y\)
Drill 2
Question: 7
Page: 498
Question: 7
Page: 498
\(\frac{3}{4}y\)larger ?
the stem is confusing!
