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If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?

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If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?  [#permalink]

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New post Updated on: 21 Sep 2019, 04:16
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If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?

A. 4
B. \(70/19\)
C. \(64/19\)
D. \(56/19\)
E. \(40/19\)

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Originally posted by abhi758 on 28 Mar 2010, 08:32.
Last edited by Bunuel on 21 Sep 2019, 04:16, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
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Re: If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?  [#permalink]

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New post 28 Mar 2010, 21:50
2
abhi758 wrote:
If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?

(a) 4
(b) \(70/19\)
(c) \(64/19\)
(d) \(56/19\)
(e) \(40/19\)

y = 3x/2
2x + 5*3x/2 = 8
x = 16/19
y = 24/19
2x+y = 32/19 + 24/19 = 56/19 hence D.
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Re: If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?  [#permalink]

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New post 16 Feb 2019, 11:06
1
abhi758 wrote:
If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?

(a) 4
(b) \(70/19\)
(c) \(64/19\)
(d) \(56/19\)
(e) \(40/19\)



Multiply 2x +5y = 8, by 3, and 3x=2y by 2

We will get 6x + 15y = 24 & 6x = 4y

19y = 24
y =24/19

x = 16/19

2*x + y = \(\frac{32}{19} + \frac{24}{19}\)

(d) \(\frac{56}{19}\)
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Re: If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?  [#permalink]

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New post 13 Dec 2019, 11:39
Hi All,

We're told that 2X + 5Y = 8 and 3X = 2Y. We're asked for the value of 2X + Y. This prompt gives us two variables and two unique equations, so it's a "System" question. There are a variety of different ways that you can approach the Algebra - and based on the answer choices, the math won't involve nice, "round" numbers (in that way that most System questions do).

I'll approach this using Substitution. Since 3X = 2Y, we know that 1.5X = 1Y. We can plug that into the first equation, which gives us...

2X + 5(1.5X) = 8
2X + 7.5X = 8
9.5X = 8
19X = 16
X = 16/19

While this is not 'pretty', it does match up with how most of the answers are written (four of the answers involve "nineteenths"). With this value of X, we can solve for Y...

3X = 2Y
3(16/19) = 2Y
48/19 = 2Y
24/19 = Y

With the value of X and the value of Y, we can answer the question that's asked:
2X + Y = ?
2(16/19) + 24/19 =
32/19 + 24/19 =
56/19

Final Answer:

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Re: If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?  [#permalink]

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New post 01 Jan 2020, 18:37
abhi758 wrote:
If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?

A. 4
B. \(70/19\)
C. \(64/19\)
D. \(56/19\)
E. \(40/19\)

PS78302.01

Project PS Butler : Question #110


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Let 2x + 5y = 8 be Eq. [1]. Rearranging the terms of the second equation, we have:

3x - 2y = 0 → Eq. [2]

Multiplying Eq. [1] by 2, we have 4x + 10y = 16. Multiplying Eq. [2] by 5, we have 15x - 10y = 0. Adding the two new equations, we obtain:

19x = 16

x = 16/19

Substituting 16/19 for x in 3x = 2y, we have:

3(16/19) = 2y

3(8/19) = y

24/19 = y

Therefore, 2x + y = 32/19 + 24/19 = 56/19.

Answer: D
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Re: If 2x + 5y =8 and 3x = 2y, what is the value of 2x + y?   [#permalink] 01 Jan 2020, 18:37
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