The variable z is directly proportional to x. When x is 11, z has the value 44. What is the value of z when x = 21?

Directly proportional, both increase/decrease, Multiple k (constant you needed to solve for) ...

Inversely - -one increases as the other decreases, increase the denominator & fraction gets smaller ... So

Problem:

Dirextly to X ( * by X)

Inversely to Y, (: by Y)

Z = k X/Y

Solve, working backwards: Z = 5 becomes

5 = k (X) : (Y). And

X=15 and Y = 9 becomes

5 = k (15) / (9). Undo : 9, * 9 both sides

45 = k (15). Now undo * 15 by : 15 both sides

45/15 = 3. So k=3, (also called your constant of variation) ... and your Equation/Proportion becomes ...

Z = 3X/Y

Use the new #s ... X=23, Y=14

Z = 3*23:14 = 69/14. If they want spirochete answer divide and round to corresponding # if decimals