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Answer:
t/r = 5/3
Step-by-step explanation:
Every proportion can be written 4 ways. I like to think of them as "upside down and sideways." They are ...
[tex]\dfrac{30}{t}=\dfrac{18}{r}\qquad\dfrac{t}{30}=\dfrac{r}{18}\\\\\dfrac{30}{18}=\dfrac{t}{r}\qquad\dfrac{18}{30}=\dfrac{r}{t}[/tex]
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Knowing this, you can simply rewrite your proportion as ...
t/r = 30/18
t/r = 5/3
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More formally, you could multiply both sides by t/18:
(30/t)(t/18) = (18/r)(t/18)
30/18 = t/r . . . . as above
Reducing the fraction gives ...
t/r = 5/3
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Additional comments
The usually-recommended procedure for solving something like this is to "cross-multiply" as a first step. That will give ...
30r = 18t
Of course, that is equivalent to multiplying both sides by rt, the product of the denominators.
From here, to get t/r, you need to divide both sides by 18r.
(30r)/(18r) = (18t)/(18r)
30/18 = t/r
The combination of the two steps, multiply by rt, divide by 18r, is equivalent to multiplying by (rt)/(18r) = t/18, as we did above. That is, you can save some work by doing both steps at once--or by simply rewriting the proportion.
