`(r-3)/(10)` = `r/14`  Solve for `r.`

Expert Answers
Payal Khullar eNotes educator| Certified Educator

`(r-3)/(10)` = `(r)/(14)`



`r` =`(5r)/(7)+3`

`r` =`(5r+21)/(7)` 

`7r` =`5r+21` 





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eddyludi | Student

(r-3)/10 = r/14

14(r-3) = 10(r)

14r-42 = 10r

14r-10r = 42

4r = 42

r = 42/4

r = 10.5

aishukul | Student

To solve this problem it is helpful to cross-multiply.

` ` = ` `  Notice in the problem, the (r-3) and the 14 are diagonal to each other. Therefore, they can be multiplied. The same happens to the r and the 10. Thus:

14 *(r-3)= 14r-42

r*10=10r. After you get these answers, the result is: 

10r=14r-42. Then, you subtract the 10r on both sides to get:

4r-42=0 Move the 42 to the other side. 


r=10.5 This is the final answer. Hope this helped!

atyourservice | Student

`(r-3)/10 = r/14 `

Multiply both sides by 10 to get rid of the fraction:

`(r-3) = (10r)/14 `

Then multiply by 14 on both sides to get rid of the other faction:

`14(r-3) = 10r `

Distribute the 14:

`14r-42 = 10r `

Now move the like terms to the same side by subtracting 14r

`-42 = 10r - 14r `

`-4r = -42`

Divide by -4 to get r alone:

`r = -42/-4`

r = 10.5

moocow554 | Student

Lets see if i can describe the process as well as the actual answer. I agree with the answer above, but i'll describe how to do it. First, you can see that this is a cross multiplication problem. Whenever a fraction = another fraction, you can cross multiply. By this, i mean that the numerator of one fraction can be multiplied by the denominator of the other  fraction. So in this case,  would be . This can be simplified to `10r = 14r-42`  . Subtract  from both sides. This leaves us with `-4r = -42` . We now can divide both sides by -4 to get "R" by itself. If you divide "-42" by "-4", you get `10.5` which can also be represented as the fraction `(21)/(2)` . Hope this Helps. 

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