FDP strategy guide Ch 7 Ratios Q-4

[RAHULZ400]

Hi Ron,

I got stuck regarding an approach for Question 4 ( DS question) in the Problem set of Ratios chapter. The question is as follows:

What is the ratio of x:y:z?

1) x+y = 2z
2) 2x+3y = z

Now I divided both the equations and got x/y = -3/5 hence y = -5/3x
I used this value in equation 1) and then solved as follows:

x-5x/3 = 2z

-2x/3=2z hence x/z = -1/3

so creating the table below

x y z
-3 5
-1 3

Multiplying upper values by 1 and lower by 3

x y z
-3 5
-3 9

so x:y:z = -3:5:9 which actually does not satisfy the equations and answer is 5:-3:1. Similarly if I substitute values in 2nd equation I get x/y = -3/5 and x/z = -1/3 and the final ratio becomes 3:5:9. The solution given takes ratio x/y and y/z and manages to get y = -3 for both ratios and then ratio is 5:-3:1 which is the appropriate answer. Kindly guide me what is wrong in my approach and how to solve it if I want the x term to be common numerator instead of y?

[RonPurewal]

hi,

• per the forum rules, please include the official answer to the problem, along with the problem itself.

Now I divided both the equations and got x/y = -3/5 hence y = -5/3x

^^ i don't understand this step -- i don't know what you mean by "i divided the equations" -- but, you apparently did something wrong, because this is incorrect.
you should have ended up with x/y = –5/3, not –3/5.

what is "dividing the equations"? perhaps if you show the work for that step, it will be easier to see why it went wrong.

__

since that step is incorrect, everything after it is invalid. (i don't know what your tables represent, either -- and, on this forum, they don't line up the way you want them to.)

[RAHULZ400]

OK. Here are the complete steps that I worked through:

1) x+y = 2z
2) 2x+3y = z

Now dividing equation 1) by 2) (this is another method of getting values):

(x+y)/(2x+3y) = 2z/z

=> x+y/2x+3y = 2

=> x+y = 2(2x+3y) = 4x+6y

=> 3x = -5y

Hence x/y = -5/3

Substituting the value of x in equation 1) we get

x+(3x/-5) = 2z

=> (-5x+3x)/-5 = 2z

=> -2x/-5 = 2z

Hence x/z = 5

Now making the table for ratios

x : y : z
-5 3
1 5

To make x common multiple multiply upper row by 1 and lower by -5 we get

x : y : z
-5 3
-5 -25

Hence the final ratio is -5:3:-25 while the actual answer is 5:-3:1. Kindly advise what is wrong with this approach and why I am unable to get the correct answer.

[RAHULZ400]

Hi Ron,

I realised I committed a careless error multiple times and thus ended up with a wrong answer. The ratio for x/z above should be 5 instead of 1/5. Hence now the table would appear as follows:

x y z
-5 3
5 1

Multiplying upper row by -1 and lower by 1

x y z
5 -3
5 1

Thus now x has common value so the ratio would be 5:-3:1.

[tim]

Looks like you've corrected your errors. I also see you've initiated a similar question on a different thread, so I'm locking this one. If you want to follow up further, please continue the discussion on that thread.