# If r varies jointly as p and q and inversely as t, then how do you find an equation for r if r=6 when p=8, q=−3, and t=3?

##### 1 Answer

Jul 30, 2017

#### Answer:

#### Explanation:

#"the initial statement is "rprop(pq)/t#

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

#"of variation"#

#rArrr=(kpq)/t#

#"to find k use the given condition"#

#r=6" when "p=8,q=-3" and "t=3#

#r=(kpq)/t#

#rArrkpq=rtlarrcolor(blue)" cross-multiplying"#

#rArrk=(rt)/(pq)=(6xx3)/(8xx-3)=18/(-24)=-3/4#

#rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(r=-(3pq)/(4t)color(white)(2/2)|)))#