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