maths help

Could someone please help me on this question?

m:n=3:8 and r is 20% of n.
work out m:r.
I keep getting 3:40 but it's wrong

To start with what's r:n ?

i think it's r:n = 1:0.2

Not quite.

Well r is 20% of n, so 1 r will go with 5 n, hence r: n is?

it's 5:1 YESSS I'VE GOT IT!! Thank you so much, the answer's 15:8. Is it also possible if you could help me on another question please??

I'm not convinced you've understood, though could by wrong, but for the benefit of other users, here's some working. Please check though.

r is 20% of n, so for every 20 r we have 100 n, and dividing through we have 1 r to 5n.

So, r:n is 1:5

and it follos that n:r is 5:1

Now m:n is 3:8.

We need the ratio of the n's to be the same in order to combine the ratios.

So, multiplying n:r as 5:1 by 8, we have n:r is 40:8

Multiplying m:n as 3:8 by 5, we have m:n is 15:40

Now we have the same ratio for n in both and can combine them.

m:n:r = 15:40:8, and hence m:r = 15:8

Apologies if that was obvious to you now.

What's your other question?

Thanks so much for this.
my other question is:
a:b = 2:3
write a in terms of b

What are your thoughts? Can you write it as a percentage?

i think it's a= 3/5b

a:b :: 2:3 means for every 2 a there are 3 b

So, for every a, there are 3/2 b

hence a=2/3 b

Notice that the fraction has inverted.

wait why does the fraction invert???

2:3 ::a:b

Putting it another way

If you have 2 a then you have 3 b

So if you have 2/3 a then you have 1 b

So for every b, there is 2/3a, i.e. the number of a's is 2/3b, i.e. a=2/3 b

This is the sort of thing that should be covered in your textbook.

yeah but you know how it's 2/3a=b and you make a the subject wouldn't it be 1b/2/3 which is 3/2b?

But it's not 2/3 a= b

Perhaps it would be elearer with a different example, suppose it's a:b :: 1:10

So, for every a there are 10 b's

So, the number of b's is 10 times the number of a's, i.e. b=10a, and

a = 1/10 b

see, i understand your example and im applying it to the previous question but I'm still getting a=3/2 b because the number of b's is 3/2 times the number of a's

If the number of b's is 3/2 times the number of a's, then the number of a's is 2/3 times the number of b's, and a=2/3b