If y varies inversely as x, how do you find x when y = 3 if y = 15 when x = 2?

1 Answer
Apr 25, 2016

Answer:

#x=10#

Explanation:

If #y# varies inversely as #x#
then
#color(white)("XXX")color(blue)(x)*color(red)(y) = color(green)(c)# for some constant #c#

We are told when #color(red)(x=2)# then #color(blue)(y=15)#
So
#color(white)("XXX")color(red)(2)*color(blue)(15)=color(green)(c)#

#color(white)("XXX")rArr color(green)(c=30)#
and
#color(white)("XXX")color(red)color(red)(x)*color(blue)(y)=color(green)(30)#

Therefore when #color(blue)(y=3)#
#color(white)("XXX")color(red)(x)*color(blue)(3)=color(green)(30)#
#color(white)("XXX")rarr color(red)(x) = 10#