Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 345

Solving equations using ratio

I'm not even sure where to start with this one.

6x^2=7xy+20y^2 where x>0 and Y>0

Find the ration of x:y

I was thinking, rearrange? Simplify? Factorise? But didn't get very far.

Again, a few hints initially would be appreciated, rather than an explanation wholesale.

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Solving equations using ratio

divide by y squared

Let z = x/y and construct a quadratic in z. z is the ratio of x to y.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Solving equations using ratio

Thanks, Bob.

This one's a challenge!

I was puzzled at;

6x^2 / y^2 = 6 (x^2/y^2)

But I think I might have understood that with a bit of work. Tell me if I'm right, please:

6 of something / something IS THE SAME AS: 6 of (the first something / the second something)?

Example:

2 of 6 / 4 = 12/4 = 3

and,

2 of (6/4) = 2 of 1.5 = 3

?

As for the rest: I'll need to take it in stages (after 2 paracetamol and a lie down )

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Prioritise. Persevere. No pain, no gain.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Solving equations using ratio

6x^2=7xy+20y^2 where x>0 and Y>0

Find the ratio of x:y

I was thinking, rearrange? Simplify? Factorise?

i tried rearranging & it helped

solve this for y in terms of x
the 'y>0' restriction will tell you which root to use
then you can do x/y but replace 'y' with the sol'n to the quadratic

interesting problem
thanks for sharing

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Solving equations using ratio

Just tackled the middle part, Bob. I wasn’t sure why
7xy divided by y^2 = 7 times x/y
I think I’ve got it now:
7xy/y^2 = 7x/y (cancel out one of the y’s on the top, and one of the y’s on the bottom)
And then 7x/y is the same as 7 times x/y (just like in the first part)
Is that right?

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Prioritise. Persevere. No pain, no gain.

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Solving equations using ratio

Thanks, amnkb,

I'll need to have a long, hard think about that one

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Prioritise. Persevere. No pain, no gain.