Answer and Step-by-step explanation:
To solve this problem, we need to use the concept of joint variation. When y varies jointly as x and z, it means that y is directly proportional to both x and z. In other words, y can be expressed as y = kxz, where k is the constant of variation.
We are given the values of y, x, and z for one situation: y = 64 when x = 4 and z = 2. Using this information, we can solve for the constant of variation, k.
64 = k * 4 * 2
64 = 8k
To solve for k, we divide both sides of the equation by 8:
8k / 8 = 64 / 8
k = 8
Now that we have the value of k, we can find y when x = 2 and z = 5.
y = k * x * z
y = 8 * 2 * 5
y = 80
Therefore, when x = 2 and z = 5, y = 80.