If x varies jointly as y and z , and x =8 when y = 4 and z=9, find z when x =16 and y =6

Hello mate!

Joint variation means that x varies with the product of z and y, then we can write this as:

x = k *(yz) where k is a real number.

we know that x is 8 when y = 4 and = 9, and with this information, we could obtain the value of k.

8 = k*(4*9) = k*(36)

then k = 8/36 = 2/9

now, if x = 16 and y = 6, we need to find the value of z, we replace the values of x and y in our equation and isolate z:

16 = (2/9)*(6z)

16 = (12/9)z

16*(9/12) = z = 12

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.