Question

How do you solve `5/13=(k-4)/39`?

Answer 1

`k=19`

Explanation:

Multiply both sides of the equation by the `color(blue)"lowest common multiple"` ( LCM) of 13 and 39

the LCM of 13 and 39 is 39

`rArrcancel(39)^3xx5/cancel(13)^1=cancel(39)^1xx(k-4)/cancel(39)^1`

`rArr15=k-4larrcolor(red)"no fractions"`

add 4 to both sides.

`15+4=kcancel(-4)cancel(+4)`

`rArrk=19`

`color(blue)"As a check"`

Substitute this value into the right side and if equal to the left side then it is the solution.

`"right side "=(19-4)/39=15/39=(cancel(15)^5)/cancel(39)^(13)`

`rArrk=19" is the solution"`