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# If 2x - y = 10 and x/ y = 3, then x =

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If 2x - y = 10 and x/ y = 3, then x =  [#permalink]

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18 Oct 2018, 02:25
2
00:00

Difficulty:

5% (low)

Question Stats:

95% (00:45) correct 5% (00:41) wrong based on 45 sessions

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If 2x - y = 10 and x/ y = 3, then x =

A. -10
B. 2
C. 4
D. 6
E. 12

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Joined: 23 May 2018
Posts: 524
Location: Pakistan
Re: If 2x - y = 10 and x/ y = 3, then x =  [#permalink]

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18 Oct 2018, 02:33
1
$$\frac{x}{y}=3$$
$$\frac{x}{3}=y$$

$$2x-y=10$$
substituting $$\frac{x}{3}$$ for $$y$$
$$2x-\frac{x}{3}=10$$
$$6x-x=30$$
$$x=6$$

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Re: If 2x - y = 10 and x/ y = 3, then x =  [#permalink]

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18 Oct 2018, 02:34
x/y = 3 ==> x = 3y
2x - y = 10
2(3y) - y = 10
y = 2
x = 3(2)
x = 6
Option D is the correct answer.

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Intern
Joined: 08 Oct 2018
Posts: 7
Re: If 2x - y = 10 and x/ y = 3, then x =  [#permalink]

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18 Oct 2018, 03:38
2
Bunuel wrote:
If 2x - y = 10 and x/ y = 3, then x =

A. -10
B. 2
C. 4
D. 6
E. 12

from above:
y=x/3
put back in equation:
2x-x/3=10
5x=30
x=6
hence D
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Re: If 2x - y = 10 and x/ y = 3, then x =  [#permalink]

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19 Oct 2018, 23:56
Equation 1: 2x-y=10 ...Eqn 1
Equation 2 $$\frac{x}{y}=3$$ ...Eqn 2
Equation 2 can be rewritten as x=3y or x-3y=0 ...Eqn 3

Multiplying (3) by 2 on both sides of the equation we have
2x-6y= 0 ..Eqn 4
From Eqn1 we have
2x-y =10 ...Eqn 5

Eqn 5 - Eqn 4

We have, 5y= 10
i.e. y=2

Substitute y=2 in Eqn 1
$$=>2x-2=10$$
$$=> 2x=12$$
$$=>x=6$$

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Re: If 2x - y = 10 and x/ y = 3, then x =   [#permalink] 19 Oct 2018, 23:56
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