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10 to 3? I don't trust my brain at 6 AM, so I don't expect it to be right

E/S = 6/2  --> E=3S
S/F = 5/3  --> 5F=3S --> F=3S/5

E/F = ?
      = 3S/(3S/5)
E/F = 5

E:F = 5:1

A shortcut for this is that you can multiply 2 and 5 which correspond to Spanish learners so it is equal to 10.
Then you multiply 5 to 6 so it equals 30 English learners.
Then you multiply 2 to 3 so it equals 6 French learners.
Then you get the ratio: 30:6 or, in lowest terms, 5:1.
(If you didn't understand the shortcut, just stick to the previous solution.)

As already explained by Miyano.. The answer 5:1 is correct.. And as she has already explained it so well.. I need not to do so. I have an suggestion for the creator of this thread. Why don't you make the topic .. Just "Maths problem" so that anybody facing one would post and another person will solve it.. Just a suggestion.. It would be fun and nice to learn.

miyano_shiho wrote: E/S = 6/2  --> E=3S
S/F = 5/3  --> 5F=3S --> F=3S/5

E/F = ?
      = 3S/(3S/5)
E/F = 5

E:F = 5:1

As expected of miyano shiho~~

easy prob thou!

I'm not good at explaining but I'll give it a try.

English : Spanish = 6:2
Spanish : French = 5:3
Since both ratios have Spanish, you have to turn the numbers for Spanish (2 and 5) into the same number. The number for Spanish then becomes 10.
For the first ratio (6:2), you multiply 2 by 5, you have to multiply 6 by 5 as well. So, it becomes 30:10.
Same goes with the second ratio. You'll get 10:6.
Then, English : Spanish : French = 30:10:6
So, English:French = 30:6 or 5:1

Well, I don't know if my explanation is understandable. Hope it is though. lol

I would just like to ask, Conan324, what grade are you in? 'Cause if you haven't had algebra yet, you won't understand my first solution. Erina's solution and my "shortcut" are essentially the same and require no algebra. If you still don't understand, just point out which part is unclear for you.

Oh, sorry if you felt bad about something I said. I didn't mean it.

You have this given: the ratio of those studying English to Spanish is 6 to 2, and Spanish to french is 5 to 3, what is the ratio to those studying English to french?

So you can form those equation out of it:
(detailed way)

(I) E : S = 6: 2      or    E/S = 6/2
(II) S : F = 5 : 3     or    S/F = 5/3

And you want to get:
E : F = ?

Now you see in (I) and (II) that both have S in it. So you form the (I) into S= ....E
Thus:
(I)  E/S = 6/2   => S= 1/3 E
Now you can insert the S into the (II) equation.

(II) S/F = 5/3 => [1/3E] /F = 5/3
Now you adjust it again: ...
And you'll get 3E =5*3F => E= 5F which is E/F = 5/1


How is that explanation for you? :V