Question

prakash ,sameer, ramesh and tarun have total 240 rs with them. Prakash has a half the total amount of what the others have. sameer has one-third of the total amount of what the others have. Ramesh has one-fourth of the total amount of what the others have.find the amount with tarun in rs?

Answer 1

I hate systems of linear equations...
BUT... we do what we must ^_^

Answer 2

We should probably represent what they have as variables.
Let's get started :D
Prakash = p
sameer = s
ramesh = r
tarun = t

Answer 3

Now, @nachi1991 based on what the problem says, what is
p + s + r + t = ?

Answer 4

amount with each of them equals 240..right?

Answer 5

That's right.
p + r + s + t = 240

four unknowns... we need exactly four equations... so we need three more.

Answer 6

Can you work out another equation?

Answer 7

Use this statement:
"Prakash has a half the total amount of what the others have. "

Answer 8

p=240/2...???

Answer 9

No... Let's break it down... after I demonstrate this, the other two will be easy :)
"Prakash has a half the total amount of what the others have"

"Prakash has..."\[\Large \color{red}p=\]
"...half..." \[\Large p = \frac12[]\]
"...the total amount of what the OTHERS have" \[\Large p = \frac12[\color{red}{r+s+t}]\]

Does that make sense to you? ^_^

Answer 10

r + s + t
is the total amount that the others have ^_^

Answer 11

ya k...so sameer will have s=1/3(p+r+t)..is it ok?

Answer 12

That's right :)
And what about Ramesh?

Answer 13

R=1/4(p+s+t)..right?..

Answer 14

Yes :)
You now have your four equations...
\[\Large p+r+s+t = 240\]\[\Large p = \frac12[r+s+t]\]\[\Large s= \frac13[p+r+t]\]\[\Large r = \frac14[p+s+t]\]
That's four equations... ^_^

Answer 15

I can see a creative way to solve this... if you're interested :)
Because I think... solving this in traditional substitution or elimination is too long and cumbersome... right @uri? XD

Answer 16

Okay, you ready? :)

Answer 17

now what do i do with these equations?

Answer 18

Let's look at these two equations first...
\[\Large p+r+s+t=240\]and\[\Large p = \frac12[r+s+t]\]
okay?

Answer 19

ya it will be great if u have some creative way to solve it..

Answer 20

Okay, look at this...
\[\Large p = \frac12[r+s+t]\]
What happens if you multiply both sides by 2?

Answer 21

Hey @nachi1991 work with me here ^_^

Answer 22

Okay, if you multiply both sides by 2, you get
\[\Large 2p = r+s+t\] right?
since 2 and 1/2 cancel out...

Answer 23

Focus :P
@nachi1991
Does this now make sense to you?
2p = r + s + t

Answer 24

ya i got it..terenzreignz..

Answer 25

hey i m sorry bt this uri is disturbing me a lot.

Answer 26

You can call me TJ.
And so, we can replace the r+s+t here:
\[\Large p + \color{red}{r+s+t}= 240\]
with 2p, since they are equal:
\[\Large p + \color{red}{2p}= 240\]
And now, you can solve for p easily ^_^

Answer 27

k TJ
yes we can replace so it will become 3p=240 i.e p=80 right?

Answer 28

That's right :D
Okay keep that in mind, p = 80.
but we won't use it.
Instead, we'll look at the third equation:
\[\Large s = \frac13[p+r+t] \]multiply both sides by 3, we get?

Answer 29

3s=p+r+t yes?

Answer 30

Indeed :)
So, we have a p + r + t here in the first equation:
\[\Large \color{red}{p+r}+s +\color{red}t=240\]
which we can replace with 3s since they are equal...
\[\Large \color{red}{3s}+s = 240\]
solve for s? :P

Answer 31

ya k so it will be s=60.

Answer 32

Correct :)
Okay, p = 80, s = 60
Now we'll use the fourth equation:
\[\Large r = \frac14[p+s+t]\] You know the drill... multiply both sides by 4, you get?

Answer 33

Sorry, I'm in a bit of a rush, so... 4r = p + s + t

Now, back to the first equation again...
\[\Large \color{red}p +r +\color{red}{s+t}=240 \]
p+s+t becomes 4r because of equality...
\[\Large \color{red}{4r}+r = 240\] so now solve for r.

Answer 34

ya so r=48....and then we have to put values of p r and right?...oh..u r awesome..thank u so much...

Answer 35

Yes. We know that p = 80, s = 60 and r = 48.
So using the first equation, you can now easily solve for t.
Do it... I have to go now :D
\[\Large p +s +r +t = 240\]\[\Large 80 + 60 + 48 + t = 240\]

I'm sure you can wrap it up now, and solve for the last variable (t)
Signing off now
---------------------------------
Terence out
^_^

Answer 36

good bye TJ..thnx