There are two straight lines
y1 = (3/7)x
y2 = (2/7)x + 343
Find "At what POSITIVE value of x, y1 reaches twice of y2 "
i am struggling with this problem from an hour... pls help using geometry only. no calculus pls.

- ganeshie8

- schrodinger

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- shubhamsrg

using geometry? maybe you mean using purely algebra?

- ganeshie8

ya solving equations... algebra is ok.. . :)

- shubhamsrg

just set y1 = 2y2
make substitutions and solve for x

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## More answers

- lgbasallote

it's not that simple lol..try it

- ganeshie8

that is giving negative x.
since these are two straight lines, there should be two values that satisfy the given condition right ?

- ganeshie8

i mean two values of x

- shubhamsrg

ok leme try
3x/7 = 4x/7 + 686
yes it gives -ve x
it has no +ve solution i'd guess..

- anonymous

no positive values only -4802

- ganeshie8

|dw:1340005766066:dw|

- shubhamsrg

why 2 solns..
see 1st eqn gives a line passing through (0,0) and slope = 3/7
2nd eqn gives a line passing through (0,343) ,slope =2/7 and both lines are increasing..
its easy to conclude then,,why only -ve x will work..

- ganeshie8

humm.. lets say x axis is time

- ganeshie8

at t=0, y2 is 343 more than y1

- anonymous

just enter the equation y1=2*(y2) and you'll see that there is only one value which is -4802.

- ganeshie8

since y1 is increasing much faster than y2, at some point y1 reaches y2

- ganeshie8

after some more time, y1 value reaches double the y2 also right ?

- ganeshie8

i need to know the time at which y1 reaches twice the value of y2.
hope my question is making sense...

- anonymous

are you sure you entered the correct equations?

- ganeshie8

there should be two values for x.. goes from \[-\infty \to + \infty\]

- ganeshie8

i am going for lunch.. brb

- shubhamsrg

well yes,,there'll be 2 values,,we didnt take the co-ordinates into account earlier,,setting y1=-2y2 will yield another solution,,but that also gives -ve x.. hmmn
there must be some explanation,,i'll get back to it..

- ganeshie8

sure there must be some explanation...

- shubhamsrg

y1/y2 = 3x/(2x + 2401) =k(say)
3x = 2kx + 2401k
=>x = 2401k/(3-2k)
so for k=3/2,,x is undefined,,k > 3/2,,x gets -ve.. k<3/2,,x is +ve..
maybe this is satisfactory,,since 2>3/2,,x had to be -ve..
but why is x -ve for k = -2//
hmm..

- shubhamsrg

maybe k is ratio of magnitudes by default,, :|

- anonymous

Much later..
I sketched the graph. It's clear that the two lines must cross. Since the relative slope (y1 grows faster than y2) is 1/7, that happens at 7 (343) = x = 2401. There, y1 = 3 (343) and y2 = 2 (343) + 343 = 1029.
However, since y2 is moving away from the x-axis with a slope of 2/7, and y1 only grows faster than y2 by 1/7, I think there is no way y1 can ever be twice y2.
Instead, at any x > 2401, (I think) y2 will be 2/3 of the way to y1 up from 1029. HTH.

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- ganeshie8

i had trouble understanding this few days back... i guess i get it finally..
frm ur explanation i see : for (y1 = 3/7x) to reach twice the value of function (y2 = 2/7x+343) --- is same as --- asking for a slope of 4/7... but y1 is slow --- its growing at 3/7 only.... so y1 can never reach twice y2.... . !! thank you :)

- anonymous

yw

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