x, y ,z, powers, algebra problems

Question

Suppose that x varies directly as y ² and inversely as z, and x is 5 when y is 3 and z is 3. What is z when x is 10 and y is 3?

Answer 1

If we use the variable k for the constant of proportionality we can set up and equation, solve for k, and then answer the question. I'll get you started

x = k (y² / z) is the equation notice x varies directly as y², inversely with z, and k is the constant to make the equality

now plug in the values given and solve for k

5 = k (3²) / 3

5 = 3k

k = 5/3

hence x = (5/3) y² / z

multiplying both sides by z and dividing by x puts the equation in the form

z = (5/3) y² / x

Now just plug the given values of 10 for x and 3 for y and you will be able to compute the answer.