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

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: D

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC 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


OA D

Source: Official Guide

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