z is directly proportional to x and y. If when x=6 and y=8, then z=48, then what is z, when x=10 and y=12?

2 Answers
Jun 14, 2017

z=120

Explanation:

z varies jointly as x and y means zpropx and zpropy i.e.

zpropx xxy

In other words z=kxx xy where k is a constant

Since when x=6 and y=8, w have z=48, we have

48=kx6xx8 and k=48/(6xx8)=48/48=1

and hence z=xy

and when x=10 and y=12

z=10xx12=120

Jun 14, 2017

z=120

Explanation:

"the initial statement is " zpropxy

"to convert to an equation multiply by k the constant of"
"variation"

rArrz=kxy

"to find k use the condition given for x, y and z"

x=6,y=8" when " z=48

z=kxyrArrk=z/(xy)=48/(6xx8)=1

rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(z=xy)color(white)(2/2)|)))

"when " x=10" and " y=12

z=10xx12=120