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505-555 (Easy)|   Algebra|      
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Bunuel
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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 10 May 2024, 01:30
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84% (01:48) correct 16% (02:45) wrong based on 258 sessions

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­If \(\frac{x}{y}=2.5\) and \(x^2 y^3 = 200\), what is the value of \(xy\)?

A. 2
B. 5
C. 6.25
D. 10
E. 32­

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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 01 Jun 2024, 05:00
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Official Solution:

If \(\frac{x}{y}=2.5\) and \(x^2 y^3 = 200\), what is the value of \(xy\)?

A. 2
B. 5
C. 6.25
D. 10
E. 32


Upon cross-multiplying \(\frac{x}{y}=2.5\), we get \(x=2.5y\). Plugging this into \(x^2 y^3 = 200\), we have \((2.5y)^2*y^3=6.25y^5=200\). Simplifying, we get \(y^5=32\), which implies \(y=2\). Then, \(x=2.5y=5\). Therefore, \(xy=10\).


Answer: D­
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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 10 May 2024, 01:52
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Bunuel
­If \(\frac{x}{y}=2.5\) and \(x^2 y^3 = 200\), what is the value of \(xy\)?

A. 2
B. 5
C. 6.25
D. 10
E. 32­
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\(\frac{x}{y}=2.5\)

\(\frac{x}{y}=\frac{5}{2}\)

\(x=\frac{5}{2}*y\)

\(x^2 y^3 = 200\)

\(\frac{25}{4}*y^2 * y^3 = 200\)

\(y^5 = 32\)

\(y = 2\)

Therefore, x = 5

x * y = 10

Option D­
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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 10 May 2024, 02:07
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Bunuel
­If \(\frac{x}{y}=2.5\) and \(x^2 y^3 = 200\), what is the value of \(xy\)?

A. 2
B. 5
C. 6.25
D. 10
E. 32­


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I think D is the answer

x/y=2.6
x^2* y^3=200

x=2.5y
(2.5y)^2*y^3=200
625/100 y^2*y^3=200

taking 100 to that side and multiplying y

625y^5= 20000

do lcm and you will get 
5^4*y^5=2^5*5^4

through this we can understand that 
y=2

putting the values
x=2.5*2
x=5

therefore
x*y=10
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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 10 May 2024, 03:06
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­As we are told that \(x^2y^3=200\)

Prime factorise \(200\) to get: \(2^3*5^2\)

From this we can assume that \(x = 5\) and \(y = 2\). To confirm, we plug these values into \(\frac{x}{y}=2.5\) and see if the equation can hold: \(\frac{5}{2}\) does equal \(2.5\).

Therefore \(xy = 10\)

ANSWER D

 
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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 10 May 2024, 04:55
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­x^2y^3=200
x^2y^3=5^2  2^3
x=5
y=2
xy=10
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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 19 Mar 2025, 15:20
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­If \(\frac{x}{y}=2.5\) and \(x^2 y^3 = 200\), what is the value of \(xy\)?

\(x^2 y^3 × \frac{x}{y} = x^3 y^2 = 200 × 2.5 = 500\)

\(x^2 y^3 × x^3 y^2 = x^5 y^5 = 200 × 500 = 100,000\)

\(xy = \sqrt[5]{100,000} = 10\)

A. 2
B. 5
C. 6.25
D. 10
E. 32­

Correct answer: D
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If x/y = 2.5 and x^2y^3 = 200, what is the value of xy? 28 Aug 2025, 11:17
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Start listing factors of 200 until you get to something cubed times something squared

8,25=2^3,5^2
5/2=2.5
xy=10 D
Bunuel
­If \(\frac{x}{y}=2.5\) and \(x^2 y^3 = 200\), what is the value of \(xy\)?

A. 2
B. 5
C. 6.25
D. 10
E. 32­

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