Final answer:
In this problem of joint variation, we can use the formula y = kxz to find the constant of variation and then calculate y for given values of x and z. By substituting the given values of y = 80, x = 8, and z = 5 into the formula, we can find the constant of variation, k, and then use it to find y when x = 3 and z = 11. The value of y is 66 when x = 3 and z = 11.
Step-by-step explanation:
Joint Variation
In this problem, we have a joint variation between y, x, and z. Joint variation occurs when a quantity varies directly with two or more other quantities, meaning that it is proportional to their product. The formula for joint variation is y = kxz, where k is the constant of variation.
Finding the Constant of Variation
To find the constant of variation, we can substitute the given values of y, x, and z into the formula and solve for k. Using the values y = 80, x = 8, and z = 5, we have:
80 = k(8)(5)
Simplifying the equation, we get:
80 = 40k
Dividing both sides by 40, we find:
k = 2
Finding y
Now that we have the value of k, we can use the formula y = kxz to find y when x = 3 and z = 11. Substituting the values into the formula, we have:
y = 2(3)(11)
Simplifying, we find:
y = 66
Therefore, when x = 3 and z = 11, y = 66.