How do you solve #\frac { 7} { k } = \frac { 25} { 15}#?

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Answer 1 · 2017-09-25T15:30:02

See a solution process below:

Because both sides of the equation are pure fractions we can "flip" the two fractions and still keep them equal:

#k/7 = 15/25#

Next, reduce the fraction on the right side of the equation:

#k/7 = (5 xx 3)/(5 xx 5)#

#k/7 = (color(red)(cancel(color(black)(5))) xx 3)/(color(red)(cancel(color(black)(5))) xx 5)#

#k/7 = 3/5#

Now, multiply each side of the equation by #color(red)(7)# to solve for #k# while keeping the equation balanced:

#color(red)(7) xx k/7 = color(red)(7) xx 3/5#

#cancel(color(red)(7)) xx k/color(red)(cancel(color(black)(7))) = (color(red)(7) xx 3)/5#

#k = 21/5# or #k = 4.2#