Question

If y varies JOINTLY as x and z, and y = 80 when x = 8 and z = 5, find y when x = 3 and z = 11​

Answer 1

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.

Answer 2

y=kxz

80=k(8)(5)

k=2 is the answer

y=kxz

y=2(3)(11)

y=1,089 is the answer