Given that y varies jointly with x and z, write the equation relating x, y, and z if y = 140 when x = 2 and z = 7.

First, write the general form for joint variation.

y = kxz

Plug in the given values for y, x, and z :

140 = k(2)(7)

Solve for k:

k = 10

Now write up that new and improved formula:

y = 10xz

Given that z varies jointly with x and y, write the equation relating z, x, and y if z = 0.06 when x = 0.3 and y = 0.2.

Careful here: this one's kinda tricky because it's z that's varying jointly with x and y. That means z goes by itself on the left of the equal sign this time, not y.

z = kxy

Plug in the given values for z, x, and y:

0.06 = k(0.3)(0.2)

Solve for k:

0.06 = 0.06k

k = 1

So z = (1)xy, or just z = xy.

Given the joint variation , find e when d = 120 and f = 9.

First off, we've gotta solve the equation for e.

Multiply both sides by :

Divide both sides by f:

Plug and chug:

e = 20