z varies directly with x and inversely with y. When x = 6 and y = 2, z = 15. Write the function that models the variation. Then, find z when x = 4 and y = 9. Write answer in a/b form if necessary.

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z varies directly with x and inversely with y hence we can write

z = kx/y ; where k is the constant of variation it is given that when x = 6 and y = 2, z = 15.
z varies jointly with x and y.

z = kx/y
15 = (6/2)k
15 = 3k
k=5
hence the relation becomes z = 5x/y
Now we need to find z = ? when x = 4 & y = 9

hence z = 5 * 4 * 9 =180 Answer

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Jun 30th, 2015

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