# If z varies directly as x and inversely as y, and z = 8 when x = 12 and y = 3, the value of the constant of proportionality is what number?

##### 2 Answers

Nov 13, 2017

#### Answer:

#### Explanation:

when z varies directly proportional to x means a division

when z varies inversely proportional to x it means a product

now with both

Nov 13, 2017

#### Answer:

#### Explanation:

#"the initial statement is "zpropx/y#

#"to convert to an equation multiply by k the constant"#

#"of variation"#

#rArrz=kxx x/y=(kx)/y#

#"to find k use the given condition"#

#z=8" when "x=12" and "y=3#

#z=(kx)/yrArrk=(yz)/x=(3xx8)/12=24/12=2#