x varies directly with y and z
x=1200,when y=20 and z=30. Find x when y=10 and z=20
x(y,z) = kyz
1200 = k*20*30
k = 2
so,
x(y,z) = 2yz
x(10,20) = 2*10*20 = 400
To find the value of x when y=10 and z=20, we can use the concept of direct variation. In direct variation, two variables, in this case, x and y, or x and z, are related by a constant ratio.
First, let's find the constant of variation between x and y. We'll use the given values:
x = 1200 when y = 20
To find the constant of variation, we divide x by y:
1200 / 20 = 60
So, the constant of variation between x and y is 60.
Now, we can use the constant of variation to find x when y=10 and z=20:
x = constant of variation * y
x = 60 * 10
x = 600
So, when y=10 and z=20, x is equal to 600.