PS: 4 equations/4 variables

Question

guys, this would be probably easy for you, but I can't seem to figure out the fastest approach to solve for any 1st variable. I can easily solve with 2 equations/2 variables, but it takes me a while to figure out equations with more than 2. I understand you must plug-in smaller equations into bigger, but I get all kinds of results that way...

can you show me your methods (fastest) to get one variable?

 h+w+d+s=78
h=w+4
d=s+2
h=7s 

Thanks.

haas_mba07 · Answer

Here's my method ..

Given 
h+w+d+s = 78 ..........(1)

h = w+4 => h-w= 4
d = s+2 => d -s = 2
--------------------------- Adding
h-w + d-s = 6
h+w+d+s= 78 .................(1)
---------------------------- Adding 
2(h+d) = 84 => d+h = 42 ............(2)

Given h = 7s

From d = s+2 => s = d-2
h= 7d - 14 or 7d-h= 14 ....(3)

From (2) & (3): 

d+h = 42
7d-h=14
-------------- Addign
8d = 56

Therefore d = 7.

u2lover · Answer

haas thanks... makes sense but takes me a bit to do it... will practice this...

do you just start working randomly with equations, or your prefer the ones with only additions first... or the ones that have different variables... or does it even matter?

f.e h=7s and h=w+4... shouldn't be touched because each is solving for h... am I right?

haas_mba07 · Answer

My guideline is to see how many variables can I eliminate at the same time i.e. by a single addition or subtraction operation. 

As for not touching an equation, it depends on what variables the eqn involves. In this case h = 7s wasn't necessary to eliminate w and s from the first equation.

 In this case adding two simple equations and eliminating the large one makes sense.

 My solution was not super quick, but took me less than a minute.. ballpark.

Hope this helps, but then again I am not an expert at Quant... so other experts will probably be more helpful.

bondguy · Answer

start with variable that touches most of the variables (if that doesn't seem to be obvious, yes , then one could use addition or subtraction between different equation to eliminate most of the variables and be left with one or two)

h+w+d+s=78
h=w+4
d=s+2
h=7s

here s has relation with d and h
so get to put everything in terms of s and see if you can get to one equation.
generally it should i dont expect that GMAT would test our mathematical proving theories than deciphering the eqations.

h = 7s 
w= 7s - 4
d= s + 2

7s + 7s - 4 + s + 2 + s = 78
16s = 80
s = 5 
h = 35
w = 31
d = 7

u2lover · Answer

no, no... this is helpful... don't be modest!!! It took me 2.5 min to try to solve it, I still didn't get the answer...

u2lover · Answer

yeah... this is the easiest way I think... very good explanations bondguy, thanks to u 2 :lol:

jaynayak · Answer

My method.....
Lets convert all into a single in this case lets convert h,d,s into w
Given 
h = w+4
7s = h => s = w+4/7
d = s+2 => d = w+4+14/7

Now put it together

w+4 + w + w+4/7 + w+18/7 = 78

=> 16w + 50 = 546
=> w = 31

netskater · Answer

Select any one variable and isolate it. Take s in this case as it appears on more than one equation

h=7s
d=s+2
w=h-4=7s-4

h+w+d+s = 7s + 7s-4 +s+2 + s = 16s - 2 = 78

therefore: s = 5

PS: 4 equations/4 variables

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