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Founder  Joined: 18 Apr 2015
Posts: 6901
Followers: 114

Kudos [?]: 1343 , given: 6316

If 3x + 2y = 24, and 7y / 2x= 7, then y = [#permalink]
Expert's post 00:00

Question Stats: 95% (01:53) correct 5% (02:04) wrong based on 20 sessions

If 3x + 2y = 24, and $$\frac{7y}{2x}$$$$= 7$$, then y =

[Reveal] Spoiler: OA
$$\frac{48}{7}$$

_________________ GRE Instructor Joined: 10 Apr 2015
Posts: 1981
Followers: 60

Kudos [?]: 1803  , given: 9

Re: If 3x + 2y = 24, and 7y / 2x= 7, then y = [#permalink]
1
KUDOS
Expert's post
Carcass wrote:

If 3x + 2y = 24, and $$\frac{7y}{2x}= 7$$, then y =

[Reveal] Spoiler: OA
$$\frac{48}{7}$$

Let's deal with 7y/2x = 7 first.
Multiply both sides by 2x to get: 7y = 14x
Divide both sides by 7 to get: y = 2x

ASIDE: At this point, I COULD take 3x + 2y = 24 and replace y with 2x to get 3x + 2(2x) = 24 and solve the equation for x. HOWEVER, the question asks us to find the value of y. So, we'd need to then take that x-value and plug it in to one of the two equations and then solve THAT equation for y.
Rather than solve an extra equation, let's do the following:

We have: y = 2x
Divide both sides by 2 to get: y/2 = x
Now, we can take 3x + 2y = 24 and replace x with y/2 to get 3(y/2) + 2y = 24 [we now have an equation that we can directly solve for y!]
Simplify: 3y/2 + 2y = 24
Multiply both sides by 2 to get: 3y + 4y = 48
Simplify: 7y = 48
Solve: y = 48/7

[Reveal] Spoiler:
48/7

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Brent Hanneson – Creator of greenlighttestprep.com  Re: If 3x + 2y = 24, and 7y / 2x= 7, then y =   [#permalink] 24 May 2017, 13:09
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