# Very hard GCSE math question

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#1
the ratio (y+x) : (y-x) is equivalent to k:1 show that y=x(k+1)/k-1

Is this inverse proportion or something? I am doing A-level maths and tutor GCSE but still couldn't figure how to do this
0
1 year ago
#2
(Original post by JessicaAsh)
the ratio (y+x) : (y-x) is equivalent to k:1 show that y=x(k+1)/k-1

Is this inverse proportion or something? I am doing A-level maths and tutor GCSE but still couldn't figure how to do this
The ratios are equivalant, so the values in one are a multiple of the values in the other.

Ie. (y+x) = mk and (y-x) = m1, for some unknown value m.

You just need to eliminate m.

An alternative way to view it is the two ratios (y+x)/(y-x) and k/1 are the same, so just equate and rearrange.
1
1 year ago
#3
Ratios can be written as fractions so write both of them as fractions then rearrange to find y
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1 year ago
#4
rewrite as a fraction and substitute for y
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1 year ago
#5
This is quite simple. Since the two ratios are equal, you can cross multiply across the ratios to get an equation in terms of k, y and x. You then make y the subject of the formula, and simplify as mych as you can. It should go something like this:

(y+x): (y-x)
.......k:1
Cross multiplication gives you:
k*(y-x)=1*(y+x) - cross multiply
ky-kx=y+x -------- open the ()
ky-y=x+kx -------- take kx to the other side, bring y to this side
y(k-1)=x(k+1) ---- factorize out y and x on each side
y=x(k+1) --------- divide both sides by (k-1)
.....(k-1)
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#6
Oh, thanks all, I feel stupid now 🙄
Learn something new every day!
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1 year ago
#7
I'm trying to help my friend in this and I read this and I still do not understand
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1 year ago
#8
(Original post by .m..)
I'm trying to help my friend in this and I read this and I still do not understand
Oh come on, this is straightforward ratio.

Consider 300:400 is the same as the ratio k:1, find k.

That means you need to find an equivalent ratio for 300:400 where the rhs is given as "1"

So, to 'force' the rhs of 300:400 to be "1", you need to divide by 400, giving 300/400 : 1
LHS now cancels to 3/4, or 0.75 if you wish.

In the original question, force y-x to be "1", which means lhs is now (y+x)/(y-x), but you're given that this ratio is the same as k:1
which obviously means when you compare the ratios, you will have
(y+x)/(y-x) : 1 is the same as k:1

And this gives (y+x)/(y-x) = k : you've turned the ratio into an equation, because of the information given at the start.
Now, you need to rearrange this equation to make "y" the subject.
If this final part is the issue, then you need to re-visit algebra, rearranging.
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1 year ago
#9
why did the signs swap their position we've been expected to learn ratios ourselves and i can't solve this for the life of me.
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