1. ## GMAT Algebra Help

Here's a question on my GMAT study book that I really don't know how to figure out...

Could someone show me HOW to work this out? And/Or the most effective way to figure it out?

2 3
if --- + --- = 4 and xy = 5, then 3x + 2y = ?
x y

crap, the formatting isn't there...

try this
if (2/x) + (3/y) = 4 and xy = 5, then 3x + 2y

2. Multiply left handside of equation one by xy, RHS by 5. (since xy=5 we can do this and equality still holds).

We get 2y +3x = 20

3. Originally Posted by matoau
Here's a question on my GMAT study book that I really don't know how to figure out...

Could someone show me HOW to work this out? And/Or the most effective way to figure it out?

2 3
if --- + --- = 4 and xy = 5, then 3x + 2y = ?
x y

$\frac{2}{x}+\frac{3}{y}=4$

if multiply by lcd xy we get

$(xy)\left( \frac{2}{x}+\frac{3}{y} \right)=4(xy) \iff 2y+3x=4 \cdot \underbrace{xy}_{equals 5}$

so $2y+3x=20$

4. Originally Posted by Oli
Multiply left handside of equation one by xy, RHS by 5. (since xy=5 we can do this and equality still holds).

We get 2y +3x = 20
So:

2 * 5 = 10
3 * 5 = 15
------------
25

?? Not following.

5. 2/x +3/y = 4
xy=5

Multiply both sides by xy:
(xy)*(2/x + 3/y) = 4xy
Which implies:
2y + 3x = 4xy
But xy = 5 so:
2y + 3x = 4*5 = 20

6. Originally Posted by TheEmptySet
$\frac{2}{x}+\frac{3}{y}=4$

if multiply by lcd xy we get

$(xy)\left( \frac{2}{x}+\frac{3}{y} \right)=4(xy) \iff 2y+3x=4 \cdot \underbrace{xy}_{equals 5}$

so $2y+3x=20$
Oh, ok...

So to clarify...

2y + 3x = 4 (here we basically took the denominator of the others fraction)

we already know xy = 5

so we simply multiply 4 * 5 and get 20?

7. Is it this simple?

if 2/x + 3y = 4 and xy = 5, then 3x + 2y = ??

2x + 3y = 4(xy)

2y + 3x = 4(5)

2y + 3x = 20

also:
how are you making these nice equations all nice and formatted?

8. Your second line isn't true.

You have to multiply both sides of the equation by xy.

b=c

=>

ab=ac

9. That is an absolute crippler, if you don't know that you will die at a young age.

10. is there somewhere I can plug this into to see the entire problem worked out? that's the only way i'm going to be able to figure this out without a math wiz sitting right next to me.

a? b? c?

we're dealing with x & y here...

b=c

=>

ab=ac
what's this mean:
"That is an absolute crippler, if you don't know that you will die at a young age."

11. The a,b,c stuff was just showing how you manipulate equations.

You have to do the same thing to both sides, otherwise the equality doesn't hold.
Examples:
x=y implies x+5=y+5
x=y implies 3x=3y
x + y = 6 implies 6(x+y)=6*6 implies 6x + 6y = 36
Absolutely crucial you understand the above or you will never ever be able to solve any maths problems.

In your second line you wrote:
2/x + 3/y = 4 implies 3/x + 3/y = 4xy
This is not true.

You should have written:
2/x + 3/y = 4 implies (2/x + 3/y)xy = 4xy

12. Originally Posted by matoau
Is it this simple?

if 2/x + 3y = 4 and xy = 5, then 3x + 2y = ??

2x + 3y = 4(xy)

2y + 3x = 4(5)

2y + 3x = 20

also:
how are you making these nice equations all nice and formatted?

It is called La Tex and here is a link on how to use it.

http://en.wikipedia.org/wiki/Help Formula

Also if you hover you mouse over someone elses code it will show up, or you can double click on it.
Good luck.

13. The whole problem, with the logic written between lines:
We know
1. 2/x + 3/y = 4
2. xy = 5

2/x + 3/y = 4
(since a=b implies ac = bc)
=>(2/x + 3/y)xy = 4xy
(since a(b+c) = ab +ac)
=> 2xy/x + 3xy/y = 4xy
(since a/a = 1)
=> 2y + 3x = 4xy
(since xy = 5 from equation 2)
=> 2y + 3x = 4*5
(since 4*5=20)
=> 2y + 3x = 20

14. Did you edit that post that started "is it this simple..."?

I think I am going crazy, whatever. That post is absolutely correct, it is that simple. Thought you wrote something different...

15. Originally Posted by Oli
Did you edit that post that started "is it this simple..."?

I think I am going crazy, whatever. That post is absolutely correct, it is that simple. Thought you wrote something different...
i didn't edit it... so it is that simple? I edited the text directly below... 2/x + 3/x

Is it this simple?

if 2/x + 3/y = 4 and xy = 5, then 3x + 2y = ??

2x + 3y = 4(xy)

2y + 3x = 4(5)

2y + 3x = 20