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

1 Answer
Jim G.
Feb 25, 2017

#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"#

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