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# HELP watch

1. (Original post by haley3721)
Let's say the two original prices are P1 and P2. If both prices are increased by 20 they become P1 + 20 and P2 + 20. So

P1 + 20 : P2 + 20 = 5 : 2

Can you do a similar thing for the other peice of information. And do you know what to do from there?
2. (Original post by haley3721)
...
Prices a, b are in the ratio a : b ~ x : y
a + 20 : b + 20 ~ 5 : 2, so 5(b + 20) = 2(a + 20)
a - 5 : b - 5 ~ 5 : 1, so 5(b - 5) = 1(a - 5)

So b + 20 = 2a/5 + 8 => b = 2a/5 - 12
And b - 5 = a/5 - 1 => b = a/5 + 4

Equate these for a, sub back into either eqn for b. Then a : b cancels down to x : y. Note a > b, x > y.
3. I don't really get the highlighted bold/underlined/italics part.

(Original post by Physics Enemy)
Prices a, b are in the ratio a : b ~ x : y
a + 20 : b + 20 ~ 5 : 2, so 5(b + 20) = 2(a + 20)
a - 5 : b - 5 ~ 5 : 1, so 5(b - 5) = 1(a - 5)

So b + 20 = 2a/5 + 8 => b = 2a/5 - 12
And b - 5 = a/5 - 1 => b = a/5 + 4

Equate these for a, sub back into either eqn for b. Then a : b cancels down to x : y. Note a > b, x > y.
4. (Original post by haley3721)
I don't really get the highlighted bold/underlined/italics part.
They're just the same eqns from the prev lines, with factor 5 moved to the RHS and bracket expanded. I then re-arrange to get b = ...
5. (Original post by haley3721)
I don't really get the highlighted bold/underlined/italics part.
Why is there 8 though?
6. (Original post by haley3721)
Why is there 8 though?
If you divide by 5 and expand, as I said:
b + 20 = 2a/5 + (2/5)20 = 2a/5 + 8
And likewise with the other eqn.

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