Answer:
The answer is:
[tex]k = 2 \\ z = 84 \\ x = 9 \\ y = 10[/tex]
Explanation:
Mathematical Equation:
[tex]z= kxy[/tex]
Solve for the constant of variation (k):
Given:
[tex]z = 60 \\ x = 5 \\ y = 6[/tex]
Find:
[tex]k = {?}[/tex]
Formula:
[tex]z = kxy[/tex]
Solution:
[tex]60 = k(5)(6) \\ 60 = 30k \\ k = 2[/tex]
Solve for z:
Given:
[tex]k = 2 \\ x = 7 \\ y = 6[/tex]
Find:
[tex]z = {?} [/tex]
Formula:
[tex]z = kxy[/tex]
Solution:
[tex]z = (2)(7)(6) \\ z = 84[/tex]
Solve for x:
Given:
[tex]k = 2 \\ z = 72 \\ y = 4[/tex]
Find:
[tex]x = {?}[/tex]
Formula:
[tex]z = kxy[/tex]
Solution:
[tex]72 = (2)(x)(4) \\ 72 = 8x \\ x = 9[/tex]
Solve for y:
Given:
[tex]k = 2 \\ z = 80 \\ x = 4[/tex]
Find:
[tex]y = {?}[/tex]
Formula:
[tex]z = kxy[/tex]
Solution:
[tex]80 = (2)(4)(y) \\ 80 = 8y \\ y = 10[/tex]
